Question

How do you simplify `3sqrt27+4sqrt12-sqrt300`?

Answer 1

`7sqrt3`

Explanation:

`3sqrt27+4sqrt12-sqrt300`

`=3sqrt(9xx3)+4sqrt(4xx3)-sqrt(100xx3)`
`=3sqrt9sqrt3+4sqrt4sqrt3-sqrt100sqrt3`
`=(3xx3)sqrt3+(4xx2)sqrt3-10sqrt3`
`=9sqrt3+8sqrt3-10sqrt3`
`=17sqrt3-10sqrt3`
`=7sqrt3`

Answer 2

`3sqrt(27)+4sqrt(12)-sqrt(300)=7sqrt(3)`

Explanation:

To answer this question, you need to get each number to the same root. You cannot do anything with them now, but by giving them a square root in common you can simplify this expression.

This is best worked out by splitting each part of the expression up:

`3sqrt(27)=3sqrt(9*3)=3*sqrt(9)*sqrt(3)=3*3*sqrt(3)=9sqrt(3)`

In short, `3sqrt(27)=9sqrt(3)`

Similarly,

`4sqrt(12)=4sqrt(4*3)=4*sqrt(4)*sqrt(3)=4*2*sqrt(3)=8sqrt(3)`

In short, `4sqrt(12)=8sqrt(3)`

And then again:

`sqrt(300)=sqrt(100*3)=sqrt(100)*sqrt(3)=10*sqrt(3)=10sqrt(3)`

In short, `sqrt(300)=10sqrt(3)`

Putting these together we get:
`9sqrt(3)+8sqrt(3)-10sqrt(3)`
`=7sqrt(3)`