How do you find the cube root of a negative number?

To find the cube root of a negative number, take the cube root of its absolute value and then negate it.

When you are asked to find the cube root of a negative number, you are essentially looking for a number that, when multiplied by itself three times, gives the original negative number. For example, the cube root of -8 is -2 because (-2) × (-2) × (-2) = -8.

The process involves two main steps. First, ignore the negative sign and find the cube root of the positive version of the number. This is called finding the cube root of the absolute value. For instance, if you need to find the cube root of -27, you first find the cube root of 27, which is 3, because 3 × 3 × 3 = 27.

Next, you reintroduce the negative sign to your result. So, the cube root of -27 is -3. This works because (-3) × (-3) × (-3) = -27.

Remember, unlike square roots, cube roots of negative numbers are real numbers. This is because multiplying three negative numbers together results in a negative number, making it possible to have a real cube root for negative values. This property is useful in various mathematical and real-world applications, such as solving equations and modelling physical phenomena.