Simplify 9/( square root of 20x)

$\frac{9}{\sqrt{20 x}}$

Step 1

Simplify the denominator.

Rewrite $20 x$ as $2^{2} \cdot (5 x)$ .

Factor $4$ out of $20$ .

$\frac{9}{\sqrt{4 (5) x}}$

Rewrite $4$ as $2^{2}$ .

$\frac{9}{\sqrt{2^{2} \cdot 5 x}}$

Add parentheses.

$\frac{9}{\sqrt{2^{2} \cdot (5 x)}}$

Pull terms out from under the radical.

$\frac{9}{2 \sqrt{5 x}}$

Step 2

Multiply $\frac{9}{2 \sqrt{5 x}}$ by $\frac{\sqrt{5 x}}{\sqrt{5 x}}$ .

$\frac{9}{2 \sqrt{5 x}} \cdot \frac{\sqrt{5 x}}{\sqrt{5 x}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{9}{2 \sqrt{5 x}}$ by $\frac{\sqrt{5 x}}{\sqrt{5 x}}$ .

$\frac{9 \sqrt{5 x}}{2 \sqrt{5 x} \sqrt{5 x}}$

Move $\sqrt{5 x}$ .

$\frac{9 \sqrt{5 x}}{2 (\sqrt{5 x} \sqrt{5 x})}$

Raise $\sqrt{5 x}$ to the power of $1$ .

$\frac{9 \sqrt{5 x}}{2 ({\sqrt{5 x}}^{1} \sqrt{5 x})}$

Raise $\sqrt{5 x}$ to the power of $1$ .

$\frac{9 \sqrt{5 x}}{2 ({\sqrt{5 x}}^{1} {\sqrt{5 x}}^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{9 \sqrt{5 x}}{2 {\sqrt{5 x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{9 \sqrt{5 x}}{2 {\sqrt{5 x}}^{2}}$

Rewrite ${\sqrt{5 x}}^{2}$ as $5 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x}$ as ${(5 x)}^{\frac{1}{2}}$ .

$\frac{9 \sqrt{5 x}}{2 {({(5 x)}^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{9 \sqrt{5 x}}{2 {(5 x)}^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{9 \sqrt{5 x}}{2 {(5 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{9 \sqrt{5 x}}{2 {(5 x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{9 \sqrt{5 x}}{2 {(5 x)}^{1}}$

Simplify.

$\frac{9 \sqrt{5 x}}{2 (5 x)}$

Step 4

Multiply $2$ by $5$ .

$\frac{9 \sqrt{5 x}}{10 x}$

Simplify 9/( square root of 20x)

Related Questions

Support LCMGCF.com by disabling your adblocker.