Question

How do you simplify square root of 8 - the square root of 66?

Answer 1

`sqrt8-sqrt66=(2-sqrt33)sqrt2`

Explanation:

The `sqrt8` can be simplified as follows:

`8` can be factored to `8=4*2`

So, `sqrt8=sqrt(4*2)=sqrt4*sqrt2=2sqrt2`

The `sqrt66` can be factored as follows:

`sqrt66=sqrt(33*2)=sqrt33*sqrt2`

So,

`sqrt8-sqrt66=2sqrt2-sqrt33*sqrt2`

Factoring out the `sqrt2` we get:

`2sqrt2-sqrt33*sqrt2=(2-sqrt33)sqrt2`

Recall: `bsqrta-csqrta=(b-c)sqrta`