How do you rationalize the denominator and simplify #6/(sqrt(20x))#?

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Answer 1 · 2017-06-10T02:54:36

See a solution process below:

First, rewrite this expression as to simplify as:

#6/(sqrt(4 * 5x)) => 6/(sqrt(4) * sqrt(5x)) => 6/(2sqrt(5x)) =>#

#3/sqrt(5x)#

To rationalize the denominator we multiply by:

#3/sqrt(5x) xx sqrt(5x)/sqrt(5x) =>#

#(3sqrt(5x))/(5x)#

Answer 2 · 2017-06-10T03:18:03

#6/sqrt(20x)=color(blue)((3sqrt5)/(5x)#

Simplify.

#6/sqrt(20x)#

Rationalize the denominator by multiplying the numerator and denominator by #sqrt(20x)/sqrt(20x)#.

#(6xxsqrt(20x))/(sqrt(20)xxsqrt(20x))#

Simplify.

#(6sqrt(20x))/(20x)#

Simplify the square root by prime factorization.

#(6sqrt(2xx2xx5xx x))/(20x)#

#(6sqrt(2^2xx5xx x))/(20x)#

Simplify.

#(6xx2sqrt(5x))/(20x)#

#(12sqrt(5x))/(20x)#

#4# goes into both #12# and #20#.

Simplify by dividing the numerator and denominator by #4#.

#(12sqrt5-:4)/(20x-:4)#

Simplify.

#(3sqrt5)/(5x)#