Find the square root of 96.(1 point) Responses 46–√ 4 start root 6 end root 64–√ 6 start root 4 end root 24 24 166–√ 16 start root 6 end root
The correct response is: √96 ≈ 9.8
not one of the choices
Apologies for the confusion. Let's calculate the square root of 96.
√96 = √(16 * 6)
= √16 * √6
= 4√6
So, the square root of 96 is 4√6.
To find the square root of 96, you can follow these steps:
1. Start by prime factorizing 96: 96 = 2^5 * 3^1.
2. Group the factors in pairs and take out one factor from each pair: √(2^4 * 3 * 2) = 2^2 * √(3 * 2) = 4√6.
3. Simplify the square root: 4√6 is the simplified square root of 96.
Therefore, the square root of 96 is 4√6.
To find the square root of 96, you can use the method of prime factorization.
Step 1: Prime Factorization of 96
- Divide 96 by its smallest prime factor, which is 2.
96 ÷ 2 = 48
- Divide 48 by 2 again.
48 ÷ 2 = 24
- Divide 24 by 2 again.
24 ÷ 2 = 12
- Divide 12 by 2 again.
12 ÷ 2 = 6
- Divide 6 by 2 again.
6 ÷ 2 = 3
Now, we have the prime factorization of 96: 2 × 2 × 2 × 2 × 3
Step 2: Group the factors into pairs of two.
- Taking two identical factors and multiplying them together allows us to take their square root.
- In this case, we have two pairs of 2's and one 3.
Now we can simplify the square root:
Square root of (2 × 2 × 2 × 2 × 3) = (2 × 2) × (√(2 × 3)) = 4√6
So, the square root of 96 is 4√6.