To divide square roots, you can multiply the numerator and denominator by the conjugate of the denominator.
In this case, we have:
32√24 / 8√6
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of 8√6, which is 8√6.
(32√24)(8√6) / (8√6)(8√6)
Simplifying the numerator:
(32)(8)√(24)(√6) = 256√(24)(√6) = 256√(24 * 6) = 256√(144)
Simplifying the square root:
256√(144) = 256 * 12 = 3072
Therefore, 32√24 / 8√6 is equal to 3072.
32\sqrt(24)-:8\sqrt(6)
5 answers
32\sqrt(24)-:8\sqrt(6) A. 4√24 / √6 B. 4√4 C. √28 / √14 D. 4√4 / √6
To divide square roots, we can multiply the numerator and denominator by the conjugate of the denominator.
In this case, we have
(32√24) / (8√6)
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of 8√6, which is 8√6.
((32√24) * (8√6)) / ((8√6) * (8√6))
Simplifying the numerator:
(32 * 8)√(24 * 6) = 256√(24 * 6) = 256√(144)
The square root of 144 is 12, so:
256√(144) = 256 * 12 = 3072
Therefore, (32√24) / (8√6) is equal to 3072.
The correct answer is not among the options provided.
In this case, we have
(32√24) / (8√6)
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of 8√6, which is 8√6.
((32√24) * (8√6)) / ((8√6) * (8√6))
Simplifying the numerator:
(32 * 8)√(24 * 6) = 256√(24 * 6) = 256√(144)
The square root of 144 is 12, so:
256√(144) = 256 * 12 = 3072
Therefore, (32√24) / (8√6) is equal to 3072.
The correct answer is not among the options provided.
choose one that is equal to and explain
Based on the options provided, option B is the closest equivalent expression:
B. 4√4
To simplify this expression, we can simplify the square root:
√4 = 2
Therefore, 4√4 = 4 * 2 = 8.
Explanation: Although this expression is not exactly equal to the original expression, it is the closest equivalent among the options provided. The original expression was (32√24) / (8√6), which simplifies to 3072. However, option B is the only option that simplifies to a whole number, which is 8.
B. 4√4
To simplify this expression, we can simplify the square root:
√4 = 2
Therefore, 4√4 = 4 * 2 = 8.
Explanation: Although this expression is not exactly equal to the original expression, it is the closest equivalent among the options provided. The original expression was (32√24) / (8√6), which simplifies to 3072. However, option B is the only option that simplifies to a whole number, which is 8.