Simplify ( square root of 9x^2)÷( square root of 5x)

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

Step 1

Rewrite the division as a fraction.

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

Step 2

Combine $\sqrt{9 x^{2}}$ and $\sqrt{5 x}$ into a single radical.

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

Step 3

Reduce the expression $\frac{9 x^{2}}{5 x}$ by cancelling the common factors.

Factor $x$ out of $9 x^{2}$ .

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

Factor $x$ out of $5 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Rewrite $\sqrt{\frac{9 x}{5}}$ as $\frac{\sqrt{9 x}}{\sqrt{5}}$ .

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

Step 5

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

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

Pull terms out from under the radical.

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

Step 6

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

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

Step 7

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 8

Combine using the product rule for radicals.

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

Simplify ( square root of 9x^2)÷( square root of 5x)

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