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

2 Answers
smendyka
Jun 10, 2017

See a solution process below:

Explanation:

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)

Meave60
Jun 10, 2017

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

Explanation:

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)

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