# How do you simplify root(3)(3000)?

Jul 23, 2015

You check to see if you can find a perfect cube to extract from the cube root.

#### Explanation:

Since $3000$ is not a perfect cube itself, you're going to have to find a way of writing this number as a product between a perfect cube and another number.

In this case, you can write $3000$ as being

3000 = 1000 * 3 = 100 * 10 * 3 = 10 * 10 * 10 * 3 = 10""^3 * 3

This means that the cube root can be simplified as

root(3)(3000) = root(3)(10""^3 * 3)

root(3)(3000) = root(3)(10""^3) * root(3)(3) = color(green)(10 * root(3)(3))