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

1 Answer
Jul 16, 2015

Answer:

#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#