Question

How do you simplify `sqrt75+sqrt108`?

Answer 1

In cases like this it often helps to factorize first.

Explanation:

Factorizing means you write a number in the form of a multiplication of smaller numbers (primes).
So you can write:

`75=3*5*5` and `108=2*2*3*3*3`

Now isolate the squares:
`75=3*5^2` and `108=3*2^2*3^2`

You can simplify by taking the squares from under the root (where they are unsquared of course):

`sqrt75+sqrt108=sqrt(3*5^2)+sqrt(3*2^2*3^3)=`

`5*sqrt3+2*3*sqrt3=5sqrt3+6sqrt3=11sqrt3`