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

2 Answers
Nov 12, 2015

=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

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