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

Question

2812 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-16T15:09:39

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

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: $bsqrta-csqrta=(b-c)sqrta$