Question

How do you simplify `4sqrt18 - 7 sqrt72`?

Answer 1

`sqrt18=sqrt9sqrt2=3sqrt2`

`sqrt72=sqrt36sqrt2=6sqrt2`

So `4sqrt18-7sqrt72=12sqrt2-42sqrt2=-30sqrt2`

Answer 2

`-30sqrt2`

Explanation:

Since `72=4*18`, we can rewrite `sqrt72` as `sqrt4sqrt72`. We now have

`4sqrt18-7sqrt4sqrt18`

This can be simplified further to

`4sqrt18-14sqrt18`

Next, we can factor out a `sqrt18` to get

`(4-14)sqrt18=-10sqrt18`

Similar to how we simplified `sqrt72`, we can simplify `sqrt18`, rewriting it as `sqrt9sqrt2`. We now have

`-10sqrt9sqrt2`, which simplifies to

`-30sqrt2`

Hope this helps!