Question

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

Answer 1

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`