Question

How do you simplify `4 sqrt 3 - sqrt 64 + 6 sqrt 27`?

Answer 1

`22sqrt3−8`

Explanation:

We know that `sqrt 64 = 8`, so we have

`4sqrt3−8+6sqrt27`

Now let's rewrite `sqrt27` as `sqrt(9)*sqrt3`
since we know the square root of 9, we can write it as `3sqrt3`

Now just a bit of simple multiplication and combining link terms
`4sqrt3−8+6(3sqrt3)`

`4sqrt3−8+18sqrt3)`

`22sqrt3−8`

Answer 2

22sqrt[3] -8

Explanation:

We can simplify first by solving sqrt[64] since we know it is a perfect square. This leaves:

4sqrt[3] -8 + 6sqrt[27]

Then we need to see if we can simplify the square roots.

4sqrt[3] is as simplified as it gets.
6sqrt[27] can be broken up into factors so:

6sqrt[27] = 6sqrt[3*9]

9 is a perfect square so it can be rooted and brought out side of the square root. This leaves:

6(3)sqrt[3]

So now we have:

4sqrt[3] -8 + 18sqrt[3]

Combine terms:

22sqrt[3] - 8