How do you simplify #sqrt(100y^2z^4)#?

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Answer 1 · 2015-11-07T15:30:19

#=color(blue)(10yz^2#

#sqrt(100y^2z^4)#

First we simplify #100# by prime factorisation(express a number as a product of its prime factors):

#100=2*2*5*5=color(purple)(2^2*5^2#

So,
#sqrt(100y^2z^4)=sqrt(color(purple)(2^2*5^2) *y^2*z^4)#

#=sqrt(color(purple)(2^2*5^2) *color(blue)(y *y) *color(green)(z^2*z^2)#

#=2*5*y*z^2#

#=color(blue)(10yz^2#