Question

How do you simplify `2\sqrt{32}-\sqrt{18}`?

Answer 1

`5sqrt2`

Explanation:

Let's factorize each of the numbers in the square roots:

`32 = 2 * 2 * 2 * 2 * 2 = 2 * 4^2`
`18 = 2 * 3 * 3 = 2 * 3^2`

So their square roots are
`sqrt32 = 4 * sqrt(2)` and `sqrt18 = 3 * sqrt2`

Therefore,
`2sqrt32 - sqrt18 = 2 * 4 * sqrt2 - 3 * sqrt2 = 5 sqrt2`

To check numerically, if we plug this into a calculator we get
`2sqrt(32) approx 11.31`, `sqrt18 approx 4.24`, and `5sqrt2 approx 7.07` and we see that `11.31 - 4.24 = 7.07` as expected.

Answer 2

`5sqrt2`

Explanation:

`2sqrt32-sqrt18`

`:.=2sqrt(4*4*2)-sqrt(2*3*3)`

`:.sqrt3*sqrt3=3`

`:.sqrt4*sqrt4=4`

`:.=2*4sqrt2-3sqrt2`

`:.=8sqrt2-3sqrt2`

`:.=5sqrt2`