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

1 Answer
Dec 21, 2015

Answer:

#=color(blue)(60sqrt3#

Explanation:

#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#