How do I factor √45a^2b and get an exact answer?

Question

How do I factor √45a^2b and get an exact answer?

Answer 1

I am guessing that what you are asking for is the sqrt(45(a^2)b), and you want to reduce it.  First, find all the factors:

sqrt(3*3*5*a*a*b)

so then what you really have is:

sqrt(3)*sqrt(3)*sqrt(5)*sqrt(a)*sqrt(a...

when you multiply a squareroot of a number by itself, you get just the number, so what you really have is:

3*sqrt(5)*a*sqrt(b)

re-written:

3a*sqrt(5b)