How do you find the cube roots root3(125)?

1 Answer
Nov 30, 2016

The answer is 5

Explanation:

x is a Real number and n is a Natural number bigger than 0
(n=1, 2, 3, 4, ...)

  • If x>=0 and n>0 (odd or even)

The rule is : rootn(x^n)=x

For example : root2((5,3)^2)=5,3 or root7((2/3)^7)=2/3

  • If x<0 and n is an odd number

We'll have instead : rootn((-x)^n)=-rootn(x^n)=-x

For example : root3((-3)^3) = -3

In this example, we need to write 125 in a form of x^3, since we have n=3, to do so we must think of writing it as a product of prime factors.

The smallest prime number that can divide 125 is 5

125/5=25

So 125=25xx5=5xx5xx5=5^3

Now that you found the form x^3, apply the rule :

root3(125)=root3(5^3)=5