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

2 Answers
Nov 12, 2015

Answer:

#=color(blue)(4#

Explanation:

#(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#

Nov 12, 2015

Answer:

#4#

Explanation:

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#