Question

How do you simplify `sqrt125 + sqrt80`?

Answer 1

The result is `9sqrt(5)`.

Explanation:

When you want to simplify the roots, the best thing you can do is to write the factors of your numbers. In your case `125=5*5*5` and `80=2*2*2*2*5`.
The square root is an operation that if you have the same numbers, gives you back one of the two numbers.
As an example `sqrt(4*4)=4`.
So we apply this property of the square root grouping the numbers in pairs (when possible) and removing from the square root:

`sqrt(125)=sqrt(5*5*5)=sqrt((5*5)*5)=5sqrt(5)`
Here I grouped a pair of `5` and I applied the rule of the square root. Unfortunately the last `5` is alone and I have to live it under the root. Now for the second term

`sqrt(80)=sqrt(2*2*2*2*5)=sqrt((2*2)*(2*2)*5)=2*2*sqrt(5)=4sqrt(5)`

Again I extracted the pairs from the root.

Finally I have: `sqrt(125)+sqrt(80)=5sqrt(5)+4sqrt(5)=9sqrt(5)`.