Simplify square root of 5/(x^2)* square root of (x^2)/45

$\sqrt{\frac{5}{x^{2}}} \cdot \sqrt{\frac{x^{2}}{45}}$

Rewrite $\frac{5}{x^{2}}$ as ${(\frac{1}{x})}^{2} \cdot 5$ .

Factor the perfect power $1^{2}$ out of $5$ .

$\sqrt{\frac{1^{2} \cdot 5}{x^{2}}} \cdot \sqrt{\frac{x^{2}}{45}}$

Factor the perfect power $x^{2}$ out of $x^{2}$ .

$\sqrt{\frac{1^{2} \cdot 5}{x^{2} \cdot 1}} \cdot \sqrt{\frac{x^{2}}{45}}$

Rearrange the fraction $\frac{1^{2} \cdot 5}{x^{2} \cdot 1}$ .

$\sqrt{{(\frac{1}{x})}^{2} \cdot 5} \cdot \sqrt{\frac{x^{2}}{45}}$

Pull terms out from under the radical.

$\frac{1}{x} \sqrt{5} \cdot \sqrt{\frac{x^{2}}{45}}$

Combine $\frac{1}{x}$ and $\sqrt{5}$ .

$\frac{\sqrt{5}}{x} \cdot \sqrt{\frac{x^{2}}{45}}$

Rewrite $\frac{x^{2}}{45}$ as ${(\frac{x}{3})}^{2} \frac{1}{5}$ .

Factor the perfect power $x^{2}$ out of $x^{2}$ .

$\frac{\sqrt{5}}{x} \cdot \sqrt{\frac{x^{2} \cdot 1}{45}}$

Factor the perfect power $3^{2}$ out of $45$ .

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

Rearrange the fraction $\frac{x^{2} \cdot 1}{3^{2} \cdot 5}$ .

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

Rewrite $\sqrt{\frac{1}{5}}$ as $\frac{\sqrt{1}}{\sqrt{5}}$ .

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

Cancel the common factor of $\sqrt{5}$ .

Cancel the common factor.

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

Rewrite the expression.

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

Combine $\sqrt{1}$ and $\frac{1}{x}$ .

$\frac{\sqrt{1}}{x} \cdot \frac{x}{3}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{\sqrt{1}}{x} \cdot \frac{x}{3}$

Rewrite the expression.

$\sqrt{1} \frac{1}{3}$

Combine $\sqrt{1}$ and $\frac{1}{3}$ .

$\frac{\sqrt{1}}{3}$

Any root of $1$ is $1$ .

$\frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$

Simplify square root of 5/(x^2)* square root of (x^2)/45

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