Question

Find the cube roots for each number:
\sqrt{327}
\sqrt{374} - Estimate

Answer 1

To find the cube root of a number, we need to find a number that, when multiplied by itself twice, equals the given number.

To find the cube root of 327, we need to find a number x such that x^3 = 327. Let's estimate the value.

Since 7^3 = 343, which is greater than 327, we can start with a smaller value.

Let's try x = 6.
6^3 = 6 * 6 * 6 = 216, which is less than 327.

Let's try x = 7.
7^3 = 7 * 7 * 7 = 343, which is greater than 327.

Therefore, the cube root of 327 is between 6 and 7. Let's estimate it to be 6.5.

To find the cube root of 374, we can follow a similar process.

Since 7^3 = 343, which is less than 374, we can start with a larger value.

Let's try x = 8.
8^3 = 8 * 8 * 8 = 512, which is greater than 374.

Therefore, the cube root of 374 is less than 8. Let's estimate it to be 7.8.

Answer 2

really?
7^3 = 343
8^3 = 512
so ∛374 will be much closer to 7 than to 8.
I'd guess about 7.2

Answer 3

You are correct, I apologize for the error. Let's try to find a more accurate estimate for the cube root of 374.

Let's try x = 7.2.
7.2^3 = 7.2 * 7.2 * 7.2 = 373.248, which is close to 374.

Therefore, the cube root of 374 is approximately 7.2. Thank you for catching that mistake.