The trick to this problem is to realize that sqrt(xy)√xy can be simplified if either xx or yy is a perfect square. So, if we have sqrt(16y)√16y, and we know that the square root of 16 is 4, we can rewrite this as 4sqrty4√y. Do you see? We need to do some factoring to get rid of all of the perfect squares under the sqrt√ sign, until we're left with a number that isn't a perfect square.
So, for the problem sqrt162√162, can we remove any perfect squares? If we think for a moment, we can see that 162 = 81 * 2162=81⋅2, and 81 is a perfect square (9x9=819x9=81). So this can be rewritten as
sqrt((81)*(2))√(81)⋅(2)
We can take the square root of 81 to get:
9sqrt(2)9√2
which is as simplified as we can get in this case.
