Find the cubic root of 96. (1 point)
O 2 * root(7, 3)
O 4sqrt(6)
2 * root(12, 3)
O 2sqrt(12)
To find the cubic root of 96, you need to find a number that, when multiplied by itself three times (cubed), equals 96. Here are the given answer choices and the steps to find the cubic root:
- Option A: 2 * root(7, 3)
This option involves taking the cube root of 7 and then multiplying the result by 2. However, 96 cannot be expressed as the cube of any number multiplied by 7, so this is not the correct answer.
- Option B: 4sqrt(6)
This option involves taking the square root of 6 and then multiplying the result by 4. However, the prompt asks for the cubic root, not the square root. So this is also not the correct answer.
- Option C: 2 * root(12, 3)
This option involves taking the cube root of 12 and then multiplying the result by 2. To check if this option is correct, we need to calculate the cube root of 12. The cubic root of 12 can be approximated to 2.289. Multiplying 2.289 by 2 gives us approximately 4.577, so this is not the correct answer.
- Option D: 2sqrt(12)
This option involves taking the square root of 12 and then multiplying the result by 2. However, the prompt asks for the cubic root, not the square root. So this is also not the correct answer.
Therefore, none of the given answer choices accurately provide the cubic root of 96.
To find the cubic root of 96, you can express it as a product of its prime factors. The prime factorization of 96 is 2^5 * 3.
Now, to find the cubic root, we can divide the exponents of the prime factors by 3 since we are looking for the cubic root.
Dividing the exponent of 2 by 3 gives us 2^5 / 3 = 2^2 = 4.
Dividing the exponent of 3 by 3 gives us 3 / 3 = 1.
Therefore, the cubic root of 96 is equal to 4 * sqrt(1).
So, the correct answer is 4sqrt(1).