How do you simplify square root of -10 times the root of -40?

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Answer 1 · 2015-09-10T10:12:55

#sqrt(-10) * sqrt(-40) = color(green)(20#

square root of -10 times the root of -40 can be written as :

#sqrt(-10) * sqrt(-40)#

One of the rules in Exponents says that #color(blue)(sqrta*sqrtb=sqrt(ab)#

Hence #sqrt(-10) * sqrt(-40) = sqrt(-10*-40)#

#=sqrt(400)#

#=sqrt(20*20)#

#=color(green)(20#

PS: It can also be equal to #-20#, but #color(green)(20# is the principal square root.