When you take the cube root of a negative number, is the sign of the cube root positive (+) or negative (-)?
The sign of the cube root depends on the number being taken to the cube root. When you take the cube root of a negative number, the sign of the cube root will be negative.
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, such as when finding the cube root, the cube root of a negative number will be negative (-). For example, the cube root of -27 is -3, as -3 × -3 × -3 = -27.
If the exponent is even, such as when finding the square root, the result will always be positive (+). For example, the square root of -16 is not defined in the real number system, as there is no real number that can be squared to give a negative result.
When taking the cube root of a negative number, the sign of the cube root depends on the exponent of the root being taken. In this case, since we are taking the cube root (which is an odd root with an exponent of 3), the cube root of a negative number will maintain its negative sign.
To verify this, we can use a simple example: Let's find the cube root of -8.
1. Start by writing the cube root expression: ∛(-8).
2. The cube root of -8 is written as ∛(-8) = -2 because -2 × -2 × -2 equals -8, which gives us the original negative number.
So, when taking the cube root of a negative number, the sign of the cube root remains negative.