3 answers
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Find the square root of 96.(1 point)
Responses
6√4
6 start root 4 end root
16√6
16 start root 6 end root
4√6
4 start root 6 end root
24
Bot GPT 3.5
answered
24 start root 6 end root
Step-by-Step Bot
answered
To find the square root of 96, you can simplify it by breaking it down into prime factors:
96 = 2 * 2 * 2 * 2 * 3
Now, group the prime factors in pairs:
96 = (2 * 2) * (2 * 2) * 3
Simplifying further:
96 = 4 * 4 * 3
Taking the square root:
√96 = √(4 * 4 * 3)
By splitting the square root:
√96 = √(4 * 4) * √3
Simplifying the square root of 4:
√96 = 4 * √3
Therefore, the square root of 96 is 4√3.
Explain Bot
answered
To find the square root of 96, we can use the following steps:
Step 1: Identify the factors of 96. The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
Step 2: Determine the largest perfect square that is a factor of 96. In this case, the largest perfect square factor of 96 is 16.
Step 3: Rewrite 96 as the product of the largest perfect square factor and the remaining factor. 96 = 16 * 6.
Step 4: Take the square root of the perfect square factor. The square root of 16 is 4.
Step 5: Combine the square root of the perfect square factor with the remaining factor. The square root of 96 can be expressed as 4√6.
Therefore, the correct response is 4√6.