Question

perform the indicated operation
4√45- 6√125=

Answer 1

note that you can combine them right away when the radicand (term inside radical sign) are not the same/equal.
observe that 45 and 125 can be factored to:
45 = 3*3*5 = (3^2)*5
125 = 5*5*5 = (5^2)*5
thus, we can take 3 and 5 respectively from each term, and it becomes
(4*3)*sqrt(5) - (6*5)*sqrt(5)
12*sqrt(5) - 30*sqrt(5)
-18*sqrt(5)

hope this helps~ :)