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

Jun 10, 2017

See a solution process below:

#### Explanation:

First, rewrite this expression as to simplify as:

$\frac{6}{\sqrt{4 \cdot 5 x}} \implies \frac{6}{\sqrt{4} \cdot \sqrt{5 x}} \implies \frac{6}{2 \sqrt{5 x}} \implies$

$\frac{3}{\sqrt{5 x}}$

To rationalize the denominator we multiply by:

$\frac{3}{\sqrt{5 x}} \times \frac{\sqrt{5 x}}{\sqrt{5 x}} \implies$

$\frac{3 \sqrt{5 x}}{5 x}$

Jun 10, 2017

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

#### Explanation:

Simplify.

$\frac{6}{\sqrt{20 x}}$

Rationalize the denominator by multiplying the numerator and denominator by $\frac{\sqrt{20 x}}{\sqrt{20 x}}$.

$\frac{6 \times \sqrt{20 x}}{\sqrt{20} \times \sqrt{20 x}}$

Simplify.

$\frac{6 \sqrt{20 x}}{20 x}$

Simplify the square root by prime factorization.

$\frac{6 \sqrt{2 \times 2 \times 5 \times x}}{20 x}$

$\frac{6 \sqrt{{2}^{2} \times 5 \times x}}{20 x}$

Simplify.

$\frac{6 \times 2 \sqrt{5 x}}{20 x}$

$\frac{12 \sqrt{5 x}}{20 x}$

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

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

$\frac{12 \sqrt{5} \div 4}{20 x \div 4}$

Simplify.

$\frac{3 \sqrt{5}}{5 x}$