Find the square root of 96.
A. 16√6
B. 24
C. 6√4
D. 4√6
which one is right
The correct answer is:
D. 4√6
To find the square root of 96, we can simplify it step-by-step.
First, we need to find the prime factorization of 96, which is 2^5 * 3.
Next, we can group the prime factors into pairs. In this case, we have 2^2 * (2 * 3).
Taking out the pairs from under the square root, we get 4√(2 * 3).
Simplifying further, we have 4√6.
Therefore, the correct answer is option D, 4√6.
To find the square root of 96, you can follow these steps:
1. Prime factorize the number 96:
96 = 2 * 2 * 2 * 2 * 2 * 3 = 2^5 * 3
2. Group the prime factors in pairs, taking out one factor from each pair:
96 = (2 * 2) * (2 * 2) * 2 * 3 = 4 * 4 * 2 * 3
3. Simplify the expression:
96 = 16 * 2 * 3
4. Take the square root of the perfect square part:
√(16 * 2 * 3) = √16 * √2 * √3 = 4√2 * √3
Therefore, the correct answer is D. 4√6.