Question 124528
Simplify:
1) {{{5sqrt(8)-2sqrt(50)+sqrt(18)}}}
The technique to use here is to factor the quantity under the radical (the radicand) looking for perfect squares in the factors. When you do find a factor that is a perfect square, take its square root and move the result outside of the radical.
Like this:
{{{5sqrt(8) = 5sqrt(2*4)}}} the 4 is a perfect square and its square root is 2, so you can rewrite this as:
{{{5sqrt(8) = 5sqrt(2*4)}}}={{{5*2sqrt(2) = 10sqrt(2)}}}
See the idea?
{{{5sqrt(8)-2sqrt(50)+sqrt(18) = 10sqrt(2)-2sqrt(2*25)+sqrt(2*9)}}} Simplifying, we get:
{{{10sqrt(2)-10sqrt(2)+3sqrt(2)=3sqrt(2)}}}
2) Simplify:
{{{3sqrt(5)-sqrt(45)= 3sqrt(5)-sqrt(5*9)}}}={{{3sqrt(5)-3sqrt(5) = 0}}}