the square root of 3 times the square root of 15

also

the square root of 18 times the square root of 3

To multiply square roots:

sq rt of z times the sq rt of y

It would be the square root of zy

The first one is

3x15 = 45

So it's the square root of 45.

Think you can figure out the next one?

Matt

Sure! Let's apply the same multiplication rule to find the square root of 18 times the square root of 3.

First, we multiply 18 and 3 to get 18 x 3 = 54.

So, the square root of 18 times the square root of 3 is equivalent to the square root of 54.

Now, to simplify the square root of 54, we can factorize 54 into its prime factors. Breaking it down, we have 2 x 3 x 3 x 3.

Next, we group the prime factors in pairs. We have one pair of 3's and one 2 remaining. The pairs can be taken out of the square root, while the remaining factors remain inside.

Taking out the pair of 3's gives us 3 x 3 = 9. So we have the square root of 9 outside the root sign.

The remaining factor, 2, stays inside the square root

Therefore, the simplified form of the square root of 54 is 3√2.

I hope that helps!