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

1 Answer
Jul 23, 2015

Answer:

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))#