Question

What is the square root of 12 multiplied by the square root of 6?

Answer 1

`sqrt(12)sqrt(6) = 6sqrt2`

Explanation:

To evaluate `sqrt12sqrt6` we must first remember that we can join these two roots together

`sqrtasqrtb = sqrt(ab)` as long as they're not both negative, so
`sqrt12sqrt6 = sqrt(12*6)`

While we can just multiply these two, we know that `12 = 2*6`, so we know that `12*6 = 2*6*6 = 2*6^2`

Therefore `sqrt(12*6) = sqrt(2*6^2)`.
Now, since there's no additions or differences being done we can take it out of the root, but to get out it loses its square. So

`sqrt(12)sqrt(6) = 6sqrt2`

And now there's no more manipulation to be done.