How do you simplify #(6sqrt20)/(3sqrt5)#?

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Answer 1 · 2015-11-12T06:44:12

#=color(blue)(4#

#(6sqrt(20))/(3sqrt5)#

Here, we first simplify #sqrt20# , by prime factorising #20#

#sqrt20=sqrt(5*2*2)=sqrt(5*2^2) = color(blue)(2sqrt5#

The expression now becomes:

#(6sqrt(20))/(3sqrt5) =( 6* color(blue)(2sqrt5))/(3sqrt5)#

#=( 12(sqrt5))/(3sqrt5)#

#=( cancel12(cancelsqrt5))/(cancel3cancelsqrt5)#

#=color(blue)(4#

Answer 2 · 2015-11-12T06:46:35

#4#

Let's get the radical out of the denominator by doing the following:

#(6sqrt20)/(3sqrt5) * sqrt5/sqrt5#

#(6sqrt20* sqrt5)/(3*5)#

Now we can combine the roots like so:

#(6sqrt100)/(15)#

Now clean it up:

#(2sqrt100)/(5)#

#(2* 10)/(5)#

#(2* 2)/(1)#

#4#