When you take the cube root of a negative number, is the sign of the cube root positive (+) or negative (–)
When you take the cube root of a negative number, the sign of the cube root depends on whether the exponent (power) of the negative number is odd or even.
If the exponent is odd, the cube root of a negative number will be negative (–).
If the exponent is even, the cube root of a negative number will be positive (+).
For example:
The cube root of -8 is -2 because the exponent 3 is odd.
The cube root of -27 is -3 because the exponent 3 is odd.
The cube root of -64 is +4 because the exponent 3 is even.
When you take the cube root of a negative number, the sign of the cube root depends on whether the exponent is odd or even.
If the exponent is odd (e.g., cube root, fifth root), then the cube root of a negative number is negative. For example, the cube root of -27 is -3.
If the exponent is even (e.g., square root, fourth root), then the cube root of a negative number is imaginary and does not have a sign. For example, the square root of -4 is √(-4) = 2i, where 'i' represents the imaginary unit.
When you take the cube root of a negative number, the sign of the cube root will depend on whether the exponent is odd or even.
If the exponent is odd (such as finding the cube root), then the cube root of a negative number will have the opposite sign. This means that the cube root of a negative number will be negative.
To explain how to get the answer, let's take an example:
Suppose we want to find the cube root of -8.
1. First, we need to determine if the exponent is odd. In this case, the exponent is 3, which is an odd number.
2. Since the exponent is odd, the cube root of a negative number will be negative.
3. Now, we can calculate the cube root of -8, which is -2.
So, the answer is -2.
Remember, this rule applies specifically to cube roots. For other roots, such as square roots or fourth roots, the sign is determined by whether the exponent is even or odd.