Find the square root of 96.
1. 4√6
2. 24
3. 16√6
4. 6√4
The correct answer is 4√6.
To find the square root of 96, we can use the prime factorization method.
Step 1: Start with the prime factors of 96, which are 2 and 3. We can write 96 as 2^5 * 3.
Step 2: Pair the prime factors in groups of 2. We have one pair of 2's (2^2) and the remaining 2 factors as single numbers (2 * 3).
Step 3: Take the square root of each pair. The square root of 2^2 is 2, and the square root of 2 * 3 is sqrt(2) * sqrt(3).
Step 4: Simplify the square root expressions. The square root of 2 is approximately 1.414, and the square root of 3 remains the same.
Therefore, the square root of 96 is approximately 1.414√3. So, the correct answer is not provided among the options you mentioned.
To find the square root of 96, you can use a calculator or follow these steps:
Step 1: Prime Factorization
Write down the prime factorization of 96.
96 = 2^5 * 3^1
Step 2: Pair the Factors
Pair the factors in sets of two and take one number from each pair.
2^2 * (2 * 3^1) = 4 * 2√6
So, the square root of 96 is equivalent to 4 * √6, which matches option 1: 4√6.