Simplify ( square root of 15)/( square root of 9x)

$\frac{\sqrt{15}}{\sqrt{9 x}}$

Step 1

Combine $\sqrt{15}$ and $\sqrt{9 x}$ into a single radical.

$\sqrt{\frac{15}{9 x}}$

Step 2

Reduce the expression $\frac{15}{9 x}$ by cancelling the common factors.

Factor $3$ out of $15$ .

$\sqrt{\frac{3 (5)}{9 x}}$

Factor $3$ out of $9 x$ .

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

Cancel the common factor.

$\sqrt{\frac{3 \cdot 5}{3 (3 x)}}$

Rewrite the expression.

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

Step 3

Rewrite $\sqrt{\frac{5}{3 x}}$ as $\frac{\sqrt{5}}{\sqrt{3 x}}$ .

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

Step 4

Multiply $\frac{\sqrt{5}}{\sqrt{3 x}}$ by $\frac{\sqrt{3 x}}{\sqrt{3 x}}$ .

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

Step 5

Combine and simplify the denominator.

Multiply $\frac{\sqrt{5}}{\sqrt{3 x}}$ by $\frac{\sqrt{3 x}}{\sqrt{3 x}}$ .

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

Raise $\sqrt{3 x}$ to the power of $1$ .

$\frac{\sqrt{5} \sqrt{3 x}}{{\sqrt{3 x}}^{1} \sqrt{3 x}}$

Raise $\sqrt{3 x}$ to the power of $1$ .

$\frac{\sqrt{5} \sqrt{3 x}}{{\sqrt{3 x}}^{1} {\sqrt{3 x}}^{1}}$

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

$\frac{\sqrt{5} \sqrt{3 x}}{{\sqrt{3 x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{5} \sqrt{3 x}}{{\sqrt{3 x}}^{2}}$

Rewrite ${\sqrt{3 x}}^{2}$ as $3 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x}$ as ${(3 x)}^{\frac{1}{2}}$ .

$\frac{\sqrt{5} \sqrt{3 x}}{{({(3 x)}^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{5} \sqrt{3 x}}{{(3 x)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{5} \sqrt{3 x}}{{(3 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{5} \sqrt{3 x}}{{(3 x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{5} \sqrt{3 x}}{{(3 x)}^{1}}$

Simplify.

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

Step 6

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $5$ by $3$ .

$\frac{\sqrt{15 x}}{3 x}$

Simplify ( square root of 15)/( square root of 9x)

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