How do you simplify #sqrt75+sqrt108#?

1 Answer
Oct 6, 2015

Answer:

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#