multiply and simplify factoring

Question

square root 20 * square root 135. Thank you

Answer 1

sqrt(20) * sqrt(135)

That can be simplified into sqrt(20*135)

Now, factor out the contents of the square roots:

20 = 4*5
135 = 9*15 = 9*3*5

So, you have

sqrt(4*5*9*3*5)

Several of those factors can be pulled out because they are perfect squares: 4, 5*5, and 9

sqrt(4) = 2, sqrt(5*5) = 5, and sqrt(9) = 3

Now, you have 2*5*3*sqrt(3) by pulling out those factors.

That simplifies to 30*sqrt(3)