Express three square root eight times two square root two in its simplest form.
So in order to simplify this, we need to multiply these numbers. So we need to multiply the numbers outside of the square root together. So we have three times two. And we also need to multiply by the numbers that are inside the square root together. Let’s simplify inside the parentheses with multiplying. And then, we’ll multiply again.
So three times two gives us six. And square root eight times square root two is equal to the square root of 16. And the square root of 16 simplifies to be four because four times four is 16. So the square root of 16 is four. And then lastly, six times four would give us a final answer of 24.
Now, we could’ve done this another way. Three square root eight could’ve simplified right from the beginning. Beginning with simplifying the square root of eight, eight is four times two. And four is two times two. So since four is a perfect square, that actually can come outside of the square root. And since there’s already a three out there we need to take, the three times the two that’s coming out, that will be out front. And then, what’s left inside is this two. And then two square root two does not simplify because two is prime. It’s all by itself. It’s only divisible by itself and one. So three times two is six.
And now just as we did before, we multiply the numbers outside of the square root together. So we have six times two. So six times two is equal to 12. And the square root of two times the square root of two is equal to the square root of four, which is equal to two. And then 12 times two is once again equal to 24. So our final answer will be 24.