Question

How do you simplify `sqrt162`?

Answer 1

We simplify this by removing the perfect squares...

Explanation:

The trick to this problem is to realize that `sqrt(xy)` can be simplified if either `x` or `y` is a perfect square. So, if we have `sqrt(16y)`, and we know that the square root of 16 is 4, we can rewrite this as `4sqrty`. 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`, can we remove any perfect squares? If we think for a moment, we can see that `162 = 81 * 2`, and 81 is a perfect square (`9x9=81`). So this can be rewritten as

`sqrt((81)*(2))`

We can take the square root of 81 to get:

`9sqrt(2)`

which is as simplified as we can get in this case.