How do you simplify #sqrt 90 times sqrt 40 - sqrt 8 times sqrt 18#?

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Answer 1 · 2017-04-22T15:00:00

#color(blue)48#

#sqrt90 xx sqrt40-sqrt8 xx sqrt18#

#:.=sqrt(3*3*10) xx sqrt(2*2*10)-sqrt(2*2*2) xx sqrt(3*3*2)#

#:.sqrt3*sqrt3=3,sqrt2*sqrt2=2#

#:.=3sqrt10 xx 2sqrt10-2sqrt2 xx 3sqrt2#

#:.=6 xx 10-6 xx 2#

#:.color(blue)(60-12=48#

Answer 2 · 2017-04-22T19:54:26

#60-12 =48#

If you are multiplying the same roots you can combine them into one root:

Here we are multiplying square roots:

#sqrta xx sqrt b = sqrt(axxb)#

#sqrt90 xxsqrt40 - sqrt8 xxsqrt18#

In this case they multiply to give perfect squares:

#=sqrt3600 - sqrt144" "larr# find the roots

#= 60 - 12#

#=48#