When you take the cube root of a negative number, is the sign of the cube root positive (+) or negative (–)?(1 point)
The sign of the cube root of a negative number is negative (–).
When you take the cube root of a negative number, the sign of the cube root depends on whether its exponent is odd or even. If the exponent is odd, then the cube root of a negative number is negative (–). If the exponent is even, then the cube root of a negative number is positive (+).
When you take the cube root of a negative number, the sign of the cube root is negative (-).
To understand why, we need to consider the concept of even and odd roots. When we take an even root (such as square root or fourth root) of a negative number, it results in an imaginary number since no real number can be squared or raised to an even power to give a negative result. However, when we take an odd root (such as cube root) of a negative number, it results in a real number because there is a real number that can be cubed to give a negative result.
Now, let's consider the cube root of a negative number. The cube root function has the property that if x is a real number, then the cube root of -x^3 is -x. In other words, the cube root of a negative number is the negative of the cube root of its absolute value.
For example, if we take the cube root of -8, the cube root of the absolute value of 8 (which is 2) is 2. Since the original number was negative, the cube root will be negative, so the answer is -2.
So, when you take the cube root of a negative number, the sign of the cube root is negative (-).