How do you simplify #4sqrt8 - 3 sqrt2#?

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Answer 1 · 2016-07-13T09:39:43

#5sqrt(2)#

Note that #8=2xx4 = 2xx2^2#

So we have

#4sqrt(2xxcolor(red)(2^2))-3sqrt(2)#

Take the #color(red)(2^2)# outside the root making it just #color(blue)(2)#

#4xxcolor(blue)(2)sqrt(2)-3sqrt(2)" "=" "8sqrt(2)-3sqrt(2)#

#color(white)(..)#
'.........................................................
Think about #8a-3a=5a#

Instead of #a# we have #sqrt(2)# but the same process applies.
'................................................................
#color(white)(..)#

#8sqrt(2)-3sqrt(2) = 5sqrt(2)#