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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