Find the square root of 96.(1 point)
Responses
24
24
46–√
4 start root 6 end root
64–√
6 start root 4 end root
166–√
8 start root 6 end root
Find the square root of 96.(1 point)
Responses
24
24
46–√
4 start root 6 end root
64–√
6 start root 4 end root
166–√
By simplifying the square root of 96, we can split it into two parts:
Square root of 16 times the square root of 6.
The square root of 16 is 4, and the square root of 6 is not a whole number. So the square root of 96 is 4√6.
To find the square root of 96, we can use a calculator or a mathematical method called prime factorization. Let's explain how to find the square root of 96 using prime factorization.
Step 1: Prime Factorization of 96
Prime factorization means expressing a number as the product of its prime factors. Let's list the prime factors of 96:
96 = 2 * 2 * 2 * 2 * 2 * 3 = 2^5 * 3
Step 2: Grouping Factors
We can group the prime factors into pairs:
96 = (2 * 2) * (2 * 2) * 3
= 4 * 4 * 3
Step 3: Taking the Square Root
Since we grouped the prime factors into pairs, we can take one number from each pair and multiply them together.
√(96) = √(4 * 4 * 3)
= √(4) * √(4) * √(3)
= 2 * 2 * √(3)
= 4√(3)
Therefore, the square root of 96 is 4√(3).