Question

Combine. Assume that all variables represent nonnegative real numbers.
square root 75a^3 + a square root 12a

Answer 1

first you want to factor the two radicals as much as possible. you should get \[\sqrt{5\times5\times3 a ^{3}} + a\sqrt{3\times2\times2a}\]. the rule says even pairs can be pulled out of the radical, so it becomes \[5a \sqrt{3a}+2a\sqrt{3a}\] now they can be added to become \[7a \sqrt{3a}\]