Find the square root of 96.(1 point)
Responses
6√4
16√6
4√6
24
4√6
To find the square root of 96, you can break it down into its prime factors.
Prime factors of 96:
96 = 2 * 2 * 2 * 2 * 2 * 3
Now, pair the prime factors into groups of two:
96 = (2 * 2) * (2 * 2) * 3 = (2^2) * (2^2) * 3
Taking the square root of each pair:
√(2^2) * (2^2) * 3 = √(2^2) * √(2^2) * √3 = 2 * 2 * √3 = 4√3
Therefore, the square root of 96 is 4√3.
To find the square root of 96, we can use a calculator or simplify the number manually.
However, to simplify it manually, we need to break down 96 into its prime factors.
Prime factorization of 96: 2 * 2 * 2 * 2 * 2 * 3
Since there are pairs of 2s, we can take them out of the square root and leave the remaining 3 inside.
Therefore, the square root of 96 can be simplified as 4 * 2√6, or simply 8√6.
So, none of the given responses (6√4, 16√6, 4√6, 24) are correct. The correct answer is 8√6.