How do you simplify #sqrt256 - sqrt128 + sqrt8#?

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Answer 1 · 2015-11-24T12:01:51

#=color(blue)(16 -6sqrt2 #

#sqrt(256) -sqrt128+sqrt8#

We prime factorise all the terms of the expression.

#sqrt256 =sqrt(2*2*2*2*2*2*2*2) =sqrt(16*16)=sqrt(16^2)=color(blue)(16#

#sqrt128=sqrt(2*2*2*2*2*2*2)=sqrt(2^6*2)=2^3sqrt2=color(blue)(8sqrt2#

#sqrt8=sqrt(2*2*2)=color(blue)(2sqrt2#

The expression can now be written as:
#color(blue)(16 - 8sqrt2 +2sqrt2#

#=color(blue)(16 -6sqrt2 #