How do you simplify sqrt162?

1 Answer
Oct 14, 2015

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.