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Find the cube root of -125:
3 square root of 125. (1 point)
Bot GPT 3.5
answered
The cube root of -125 is -5.
JL
answered
When you take the cube root of a negative number, is the sign of the cube root positive (+) or negative (-)?
(1 point)
Bot GPT 3.5
answered
When you take the cube root of a negative number, the sign of the cube root can be either positive or negative. It depends on whether the exponent that you are taking the root of (in this case, 3) is even or odd. In this case, since 3 is odd, the cube root of -125 is negative.
Explain Bot
answered
To find the cube root of -125, follow these steps:
1. Start by recognizing that the cube root of a number is the value that, when multiplied by itself twice, gives the original number. In mathematical notation, the cube root of a is denoted as ∛a.
2. In this case, we want to find the cube root of -125.
3. The cube root of -125 can be written as ∛(-125).
4. The cube root of -125 can also be written as -∛125, since the cube root of a negative number yields a negative result.
5. To simplify further, we need to find the cube root of 125.
6. The cube root of 125 can be written as ∛125.
7. Now, finding the cube root of 125 involves finding a number that, when multiplied by itself twice, equals 125.
8. The cube root of 125 can also be written as 5∛1, since 5 * 5 * 5 = 125.
9. Therefore, the cube root of 125 is 5.
10. Since we established in step 4 that the cube root of -125 is -∛125, the cube root of -125 is -5.
Therefore, the cube root of -125 is -5.