How do you multiply # (3sqrt6)(2sqrt50)#?

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Answer 1 · 2015-12-21T16:58:09

#=color(blue)(60sqrt3#

#color(blue)(3sqrt6) xx 2sqrt50#

#= color(blue)(3 xx2) xx sqrt6 xx sqrt50#

#= color(blue)(6) xx sqrt300#

Prime factorising #300#

#300=2*2*5*5*3#

So, #sqrt300=sqrt(2*2*5*5*3)#

#=sqrt(2^2xx5^2xx3)#

#=2 xx 5sqrt( 3)#

#=10sqrt( 3)#

The expression becomes:
#= color(blue)(6) xx sqrt300 = color(blue)(6 xx 10sqrt3#

#=color(blue)(60sqrt3#