Question 153328
Simplify:
{{{3sqrt(32) - 5sqrt(50) - 8sqrt(45) + 7sqrt(20)}}}
Factor the numbers under the radicals (the radicands).
{{{3sqrt(16*2) - 5sqrt(25*2) -8sqrt(9*5) + 7sqrt(4*5)}}}
Notice that one of the factors under each radical is a perfect square.
{{{3sqrt(4^2*2) - 5sqrt(5^2*2) - 8sqrt(3^2*5) + 7sqrt(2^2*5)}}} 
So you can take the square root of these and move the result outside of the radical.
{{{3*4sqrt(2)-5*5sqrt(2)-8*3sqrt(5)+7*2sqrt(5)}}} Now perfom the indicated multiplication.
{{{(12sqrt(2)-25sqrt(2))-(24sqrt(5)-14sqrt(5))}}} Finally, combine like-terms.
{{{highlight(-13sqrt(2)-10sqrt(5))}}}...and there you have it!