Find the square root of 96.
A. 16√6
B. 24
C. 6√4
D. 4√6
The square root of 96 is approximately 9.8. None of the answer choices are equal to approximately 9.8, so the correct answer is not listed.
To find the square root of 96, follow these steps:
Step 1: Prime factorize 96.
96 can be written as 2^5 * 3.
Step 2: Group the prime factors in pairs, and take out one factor from each pair.
There are two pairs - (2^2) and (2 * 3).
Step 3: Move the factors taken out outside the square root.
The square root of (2^2) is 2, and the square root of (2 * 3) is √(2 * 3).
Step 4: Simplify the square root.
The square root of 96 simplified is 2√(2 * 3).
Therefore, the answer is option D: 4√6.
To find the square root of 96, you can simplify it by factoring out any perfect square factors from within the square root sign.
The prime factorization of 96 is 2 × 2 × 2 × 2 × 2 × 3.
Now, group the numbers inside the square root sign into pairs of equal factors: √(2 × 2 × 2 × 2 × 2 × 3).
Since there are two pairs of 2, you can take them out of the square root sign: 2 × 2 × √(2 × 3).
Simplifying further, you get: 4√(2 × 3).
Therefore, the correct answer is option D: 4√6.