How do you simplify #8sqrt(448)#?

1 Answer
Alan P.
Jan 14, 2016

#8sqrt(448) = 64sqrt(7)#

Explanation:

Extracting square factors (the only one we really use here is #2^2=4#):

#448 = 2^2xx112#
#color(white)("XX")=2^2*2^2xx28#
#color(white)("XX")=2^2*2^2*2^2xx7#

#rArr#
#sqrt(448) = sqrt(2^2*2^2*2^2*7#
#color(white)("XXX")=(2*2*2)sqrt(7)#
#color(white)("XXX")=8sqrt(7)#

Therefore
#8sqrt(448) = 8*8sqrt(7)#
#color(white)("XXXX")=64sqrt(7)#

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