Algebra and Trigonometry (5th Edition)

Chapter 12

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, 6, , , , , , , 0, ; The rational numbers are ... more

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, , , , ; The integers consist of the whole ... more

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, , , , ; The numbers which are not rational but ... more

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6, , , 0, ; The integers consist of the whole ... more

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6, , 0, ; The whole numbers consists of the ... more

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All the provided numbers ; The real numbers ... more

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Additive inverse property ;  If  is any real ... more

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Associative property of multiplication ; If , , ... more

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Distributive property ;  If ,  and  are any real ... more

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Commutative property of addition ;  If  and  be ... more

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Multiplicative identity property ;  If  is any ... more

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Commutative property of multiplication ; If  and  ... more

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Additive identity property ;  If  is any real ... more

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Multiplicative inverse property ;  If  is any real... more

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Associative property of addition ;  If ,  and  are... more

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Distributive property ;  If ,  and  are any real ... more

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98 ; If  is any real number, then it's absolute ... more

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0 ; If  is any real number, then it's absolute ... more

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; If  is any real number, then it's absolute ... more

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; If  is any real number, then it's absolute ... more

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20 ;  If  and  are any real numbers, then the ... more

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;  If  and  are any real numbers, then the ... more

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11 ; If  and  are any real numbers, then the ... more

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; If  and  are any real numbers, then the ... more

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19 ; Add the opposite of , that is, 11, to 8 to ... more

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; According to the given expression, the numbers ... more

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; According to the given expression, the dividend... more

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; Add the opposite of , that is, 1, to  to ... more

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; According to the given expression, the numbers ... more

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; Add the opposite of 5, that is, , to  to ... more

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24 ; For the addition of a positive and a negative... more

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10 ; According to the given expression, the ... more

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; According to the given expression, the numbers ... more

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20 ; Add the opposite of , that is, 33, to  to ... more

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; For the addition of a positive and a negative ... more

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; Add the opposite of , that is, , to  to ... more

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; According to the given expression, the dividend... more

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; For the addition of negative numbers, their ... more

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; According to the given expression, the dividend... more

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 Draw the number line and represent the numbers 9 ... more

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Draw the number line and represent the numbers  ... more

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Plot the number line and represent the numbers  ... more

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 As per the inequality,  is greater than or equal ... more

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Plot the number line and represent the numbers  ... more

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 Plot the number line and represent the numbers  ... more

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; The given set notation represents the set of ... more

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; The given set notation represents the set of ... more

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; The given set notation represents the set of ... more

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;  The given set notation represents the set of ... more

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; The given set notation represents the set of ... more

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; According to set notation, the given set ... more

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; The graph represents the real numbers between  ... more

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;  The graph represents the real numbers that ... more

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;  The graph represents the real numbers between... more

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; The graph represents the real numbers that ... more

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; If  is any nonzero number and  be any integer, ... more

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; If is any nonzero number and be any integer, ... more

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; If and are any nonzero numbers, and and be ... more

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; Apply the property to the expression. ; more

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; If is any nonzero number, then . So, the given... more

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; Apply the quotient rule of exponents to the ... more

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; Apply the product rule of exponents to the ... more

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; Apply the product rule of exponents to the ... more

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; Apply the property of raising a product to a ... more

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; Apply the power rule of exponents to the given ... more

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; Any number can be expressed into scientific ... more

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; Any number can be expressed into scientific ... more

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; Any number can be expressed into scientific ... more

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; Any number can be expressed into scientific ... more

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; Multiply  by , that is,  to obtain the decimal ... more

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5,170,000 ; Multiply  by , that is, 1,000,000 to ... more

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620,300,000,000 ; Multiply  by , that is, 100,000,... more

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; Multiply  by , that is,  to obtain the decimal ... more

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3 ; Divide 18 by 6 in the given expression. ; Add ... more

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103 ; Perform subtraction of the terms inside the ... more

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; Express  as 9 to simplify the exponential term... more

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2048 ; Divide 16 by 4 and 4 by 2 in the given ... more

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2 ; Express , , , and  as 64, , 1024, and  to ... more

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5 ; Subtract the terms inside the parentheses of ... more

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6 ; The sum of the exponents on the variables of a... more

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8 ; The sum of the exponents on the variables of a... more

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4 ; The sum of the exponents on the variables of a... more

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0 ; The sum of the exponents on the variables of a... more

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8 ; The sum of the exponents on the variables of a... more

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Monomial is a type of polynomial that has only 1 ... more

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; Group the similar terms of the given expression... more

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; Group the similar terms of the given expression... more

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; Group the similar terms of the given expression... more

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; Group the similar terms of the given expression... more

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; Group the similar terms of the given expression... more

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; Multiply the coefficients and the variables of ... more

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; Apply the FOIL method to multiply each term of ... more

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; Apply the FOIL method to multiply each term of ... more

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; Apply the FOIL method to multiply each term of ... more

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; Apply the FOIL method to multiply each term of ... more

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; Apply the square of a sum formula to find the ... more

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; Apply the square of difference formula to find ... more

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; Apply the square of sum formula to find the ... more

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; Apply the product of sum and a difference ... more

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; Apply the product of sum and a difference ... more

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; Express 18 as a product of 3 and 6 to rewrite ... more

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; Express  as a product of and  and  as a product... more

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; Group the first and the last two terms, ... more

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; Group the first and the last two terms, ... more

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; The trinomial is similar to the form , where  ... more

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; The trinomial is similar to the form , where  ... more

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; Factor out the common factor 2 from the given ... more

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; Factor out the common factor  from the given ... more

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; The trinomial is similar to the form, where is... more

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; The trinomial is similar to the form, where is... more

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; Express 81 as  to rewrite the given polynomial ... more

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; Express  as  and 9 as  to rewrite the given ... more

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; Factor out the largest common factor, , from ... more

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; Express 36 as  and  as a product of 2, , and 6 ... more

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; Express  as , 4 as , and  as a product of 2, , ... more

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; Factor out the largest common factor, , from ... more

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; Express 64 as to rewrite the given polynomial ... more

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; Express 216 as to rewrite the given polynomial... more

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; Take out largest common factor, from the  ... more

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; Express as and 1 as to rewrite the given ... more

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; Apply the multiplication principle to multiply ... more

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; Apply the addition principle to add 5 to both ... more

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; Apply the addition principle to add to both ... more

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; Apply the addition principle to add 15 to both ... more

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; Apply the addition principle to add to both ... more

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; Apply the addition principle to add to both ... more

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; Apply the distributive property to the left ... more

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; Apply the distributive property to the left ... more

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; Apply the addition principle of inequality to ... more

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; Apply the multiplication principle of ... more

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; Apply the addition principle of inequality to ... more

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; Apply the addition principle of inequality to ... more

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; Apply the Addition Principle of inequality to ... more

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; Apply the Addition Principle of inequality to ... more

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, ; Apply the principle of zero products in the ... more

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, ; Apply the principle of zero products in the ... more

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, ; Rewrite as a difference of and .  Factor out... more

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, ; Apply the principle of zero products in the ... more

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, ; The given equation is similar to the form , ... more

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, ; Subtract 30 from both sides of the equation ... more

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, ; Rewrite as a difference of and .  Factor out... more

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; Add 36 on both sides of the given equation and ... more

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; Add 20 on both sides of the given equation and ... more

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; Divide both sides of the given equation by 6 ... more

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; Add 15 on both sides of the given equation and ... more

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; Add 1 on both sides of the given equation and ... more

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; Add 75 on both sides of the given equation and ... more

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The set that consists of all the real numbers ... more

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The set that consists of all the real numbers ... more

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; Factor the numerator and the denominator of the... more

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; Factor the numerator and the denominator of the... more

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; Factor out  from the numerator and  from the ... more

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; Factor out 6 from the numerator and 3 from the ... more

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1 ; Multiply the numerator and the denominator of ... more

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; Multiply the reciprocal of the divisor by the ... more

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; Multiply the numerator and the denominator of ... more

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; Multiply the reciprocal of the divisor by the ... more

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; Multiply the reciprocal of the divisor by the ... more

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; Multiply the numerator and the denominator of ... more

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2 ; Add the numerators of both the rational ... more

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; Factor the denominators of both the rational ... more

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; Factor the denominator of the first rational ... more

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; Factor the denominators of both the rational ... more

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; Factor the denominator of the first rational ... more

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; Factor the denominators of both rational ... more

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; The least common denominator of the numerator ... more

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; Multiply the numerator of the given expression ... more

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; Rewrite the term  as  and 1 as .The least ... more

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; Multiply the numerator of the given expression ... more

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; The least common denominator of the numerator ... more

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21 ; As the index is even, use the property  in ... more

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; Rewrite the radicand in the given expression as... more

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; As the index is even, use the property  in the ... more

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; Rewrite the radicand in the given expression as... more

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; Rewrite the radicand in the given expression as... more

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2 ; Rewrite the radicand in the given expression ... more

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; Rewrite the number 48 as a product of 3 and 16 ... more

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; Use the property  to combine both the radicals ... more

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; Apply the property , where , to the given ... more

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; Apply the property , where , to the given ... more

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; Factor the radicand of the given expression. ; ... more

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; Use the property  in the given expression and ... more

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; Use the property  in the given expression and ... more

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; Write the number 32 as a product of 16 and 2.... more

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; Write the number 12 as a product of 4 and 3.Use... more

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;  Factor all the radicands of the given ... more

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;  Factor all the radicands of the given ... more

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; Multiply 2 by 5, 2 by ,  by 5, and  by  and add... more

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; Multiply  by ,  by ,  by , and  by  and add the... more

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; Use the formula for the square of a sum in the ... more

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; Multiply the numerator and the denominator of ... more

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; Multiply the numerator and the denominator of ... more

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; Multiply the numerator and the denominator of ... more

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; Multiply the numerator and the denominator of ... more

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; Multiply the numerator and the denominator of ... more

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; Multiply the numerator and the denominator of ... more

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; Multiply the numerator and the denominator of ... more

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; , where  and  are natural numbers and  ... more

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; , where  and  are natural numbers and  ... more

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8 ; Use the formula  to rewrite the given ... more

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128 ; Use the formula  to rewrite the given ... more

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; Use the formula  to convert the negative ... more

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; Use the formula  to convert the negative ... more

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; , where  and  are natural numbers and  ... more

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; , where  and  are natural numbers and  ... more

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; Apply the product rule for exponents to the ... more

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; Apply the product rule for exponents to the ... more

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; Apply the raising a product to a power rule to ... more

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17 ; Substitute 15 for  and 8 for  into the ... more

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; Substitute 4 for  and 4 for  into the equation ... more

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12 ; Substitute 5 for  and 13 for  into the ... more

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5 ; Substitute 12 for  and 13 for  into the ... more

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; Substitute  for  and 6 for  into the equation ... more

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