Thank you for the opportunity to help you with your question!

Firstly, in order to simplify the square root of 32, we break it down into smaller numbers.

The square root of 32 also equals the square root of (16 * 2) . Since the square root of 16 is a whole number, 4, (4 *4 =16) we can pull it out of the square root to get: 4 * sqrt (2)

Now, putting that together with the other half of the question, we have: 4 * sqrt (2) * sqrt (2) .

Any square rooted number multiplied by the square root of itself is equal to the number under the square root. --it might be easier to see it plainly: sqrt(2) * sqrt (2) = 2.

So now what we're left with is 4 *2, which is 8.

Please let me know if you need any clarification. I'm always happy to answer your questions!