How do you simplify #(sqrt2 * sqrt8)/2#?

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Answer 1 · 2015-04-09T13:01:37

#sqrt(2)# #*# 2 #sqrt(2)# #-:# 2 =

= 2

Answer 2 · 2015-04-09T13:06:46

#(sqrt2 * sqrtcolor(blue)(8))/2#

#= (sqrt2 * sqrtcolor(blue)(2^3))/2 # (We write 8 as #2^3#)

#= (sqrt2 * sqrtcolor(blue)(2^2*2))/2 # (We write #2^3# as #2^2*2#)

#= (sqrt2 * (cancel2*sqrt2))/cancel2# #(sqrt(2^2*2) =sqrt(2^2)*sqrt2)#

#= sqrt2 * sqrt2 #

#color(green)(= 2 #