sat suite question viewer

Advanced Math / Equivalent expressions Difficulty: Hard

If a and c are positive numbers, which of the following is equivalent to the square root of, open parenthesis, a plus c, close parenthesis, cubed, end root, times, the square root of a plus c, end root?

Back question 67 of 102 Next
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

Explanation

Choice C is correct. Using the property that the square root of x, end root, times the square root of y, end root, equals the square root of x y, end root for positive numbers x and y, with x = (a + c)3 and y = a + c, it follows that the square root of, open parenthesis, a, plus c, close parenthesis, cubed, end root, times, the square root of a, plus c, end root, equals the square root of, open parenthesis a, plus c, end parenthesis to the power 4, end root. By rewriting (a + c)4 as ((a + c)2)2, it is possible to simplify the square root expression as follows: the square root of, open outer parenthesis, open inner parenthesis, a, plus c, close inner parenthesis, squared, close outer parenthesis, squared, end root, equals, open parenthesis, a, plus c, close parenthesis, squared, which equals a, squared, plus 2 a, c, plus c squared.

Choice A is incorrect and may be the result of the square root of, open parenthesis, a, plus c, close parenthesis, cubed, end root, divided by the square root of, a, plus c, end root. Choice B is incorrect and may be the result of incorrectly rewriting (a + c)2 as a2 + c2. Choice D is incorrect and may be the result of incorrectly applying properties of exponents.