Question

Simplify sqrt 162 - sqrt 160 + 5 sqrt 32 - sqrt 90

-4 sqrt 56
22 sqrt 8
29 sqrt 2 - 7 sqrt 10
29 sqrt 4 - 7 sqrt 20

Answer 1

To simplify a square root, you need to factor out everything you have under the square root. To do this, usually I do a factor tree.

So for example, in sqrt 162, you have the following multiplied together:

9 * 9 * 2, all under a square root.

There are two 9's, so you can take one out, and you are left with 9 sqrt 2.

Repeat with all other terms.

in the end, you will be left with:

9 sqrt 2 - 4 sqrt 10 + 5(4) sqrt 2 - 3 sqrt 10

Square roots with the same number under the root can be treated like an x, they are both like terms.

For example, 9 sqrt 2 + 20 sqrt 2 = 29 sqrt 2.

So your answer is 29 sqrt 2 - 7 sqrt 10