Find the square root of 96.(1 point)
Responses
166–√
16 √ 6
24
46–√
Option 4: 46- √
Find the cubic root of 96.(1 point)
Responses
212−−√3 12
√ 4
27–√3 2
212−−√
Option 2: √ 4
Find the cubic root of 189.(1 point)
Responses
37–√ 3
921−−√3 9
37–√3 3
277–√3
Option 1: 37-√ 3
Find the square root of 250.(1 point)
Responses
2510−−√ 25
250
250 105–√ 10
510−−√
Option 3: 250 105-√ 10
Find the square root of 128.(1 point)
Responses
24–√ 2
82–√ 8
64 −−−√ x 2–√
42–√
Option 2: 8-√ 8
To find the square root of 96, we can use a calculator or perform the calculation manually. Here's one way to do it manually:
1. Start by finding the prime factorization of 96: 96 = 2^5 * 3^1.
2. Split the prime factors into pairs, where each pair consists of the same prime factor: (2^2 * 3^0) * (2^1 * 3^1).
3. Take one number from each pair and multiply them together: (2^2) * (2^1) = 2^3 = 8.
4. The result, 8, is the largest square number that is less than or equal to 96.
5. Divide 96 by 8: 96 / 8 = 12.
6. The square root of 96 can be written as √(8 * 12) = √8 * √12.
7. Simplify each square root individually: √8 = 2√2 and √12 = 2√3.
8. Put everything together: √(8 * 12) = √8 * √12 = 2√2 * 2√3 = 4√6.
Therefore, the square root of 96 is 4√6.