Before we can combine any like terms, we need to rationalize the denominators of the terms. At first we can rewrite every radical in the quotient as a quotient of two radicals.
8sqrt(5/4)+3sqrt(20)-10sqrt(1/5)=8sqrt(5)/sqrt(4)+3sqrt(20)-10sqrt(1)/sqrt(5)
Now, we can rationalize the denominators of these quotients. Since there is already a perfect square under the radicand in the denominator of the first term, we will simplify it at once.
To rationalize a denominator, we multiply the numerator and denominator by a radical that will eliminate the radical in the denominator. Because the denominator of the third term is a square root, we need to multiply it by a square root that will give us a perfect square under the radical.
Radicals can only be added or subtracted when they have like radicands.
a sqrt(x) + b sqrt(x) = (a+b) sqrt(x)
a sqrt(x) - b sqrt(x) = (a-b) sqrt(x)
Let's use perfect squares to simplify our radicals to see if we can create like terms.
