How do you simplify #sqrt125 + sqrt80#?

1 Answer
May 28, 2016

Answer:

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)#.