How do you simplify #3 sqrt (2) + 5 sqrt(2)#?

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Answer 1 · 2016-03-20T21:13:20

A different approach!

#8sqrt(2)" "-># as an #underline("exact")# answer

11.314 to 3decimal places as an #underline("approximate")# value

Compare to :#" " 3x+5x =8x#

Suppose that instead of #x# we had #sqrt(2)#

Just because it is a square root makes no difference. You are combining 3 of them with 5 of them

so #" "3sqrt(2)+5sqrt(2)= 8 sqrt(2)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Another way!

Common factor is # sqrt(2)#

#color(brown)(3sqrt(2)+5sqrt(2)) =color(blue)(sqrt(2)(3+5)#
#=sqrt(2)xx8 = 8sqrt(2)#