How do you simplify #2sqrt5 *3sqrt10 #?

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Answer 1 · 2015-09-06T19:50:06

#30sqrt(2)#

#color(red)(2sqrt(5))*color(blue)(3sqrt(10))#

#= color(red)(2)*color(blue)(3)*color(red)(sqrt(5))*color(blue)(sqrt(10))#

#= 6* color(green)(sqrt(50))#

#= 6* color(green)(sqrt(25)*sqrt(2))#

#=6*color(green)(5sqrt(2))#

#=30sqrt(2)#

Answer 2 · 2015-09-06T19:51:48

I found: #30sqrt(2)#

You can write:
#2sqrt(5)*3sqrt(5*2)=(2*3)sqrt(5)sqrt(5)sqrt(2)=#
Multiply:
#=6*5*sqrt(2)=#
Where you used the faxt that #sqrt(x)sqrt(x)=x#.

So: #2sqrt(5)*3sqrt(10)=30sqrt(2)#