Simplify square root of 2/x* square root of (x^2)/8

$\sqrt{\frac{2}{x}} \cdot \sqrt{\frac{x^{2}}{8}}$

Rewrite $\sqrt{\frac{2}{x}}$ as $\frac{\sqrt{2}}{\sqrt{x}}$ .

$\frac{\sqrt{2}}{\sqrt{x}} \cdot \sqrt{\frac{x^{2}}{8}}$

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

$\frac{\sqrt{2}}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}} \cdot \sqrt{\frac{x^{2}}{8}}$

Combine and simplify the denominator.

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

$\frac{\sqrt{2} \sqrt{x}}{\sqrt{x} \sqrt{x}} \cdot \sqrt{\frac{x^{2}}{8}}$

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

$\frac{\sqrt{2} \sqrt{x}}{{\sqrt{x}}^{1} \sqrt{x}} \cdot \sqrt{\frac{x^{2}}{8}}$

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

$\frac{\sqrt{2} \sqrt{x}}{{\sqrt{x}}^{1} {\sqrt{x}}^{1}} \cdot \sqrt{\frac{x^{2}}{8}}$

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

$\frac{\sqrt{2} \sqrt{x}}{{\sqrt{x}}^{1 + 1}} \cdot \sqrt{\frac{x^{2}}{8}}$

Add $1$ and $1$ .

$\frac{\sqrt{2} \sqrt{x}}{{\sqrt{x}}^{2}} \cdot \sqrt{\frac{x^{2}}{8}}$

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

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

$\frac{\sqrt{2} \sqrt{x}}{{(x^{\frac{1}{2}})}^{2}} \cdot \sqrt{\frac{x^{2}}{8}}$

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

$\frac{\sqrt{2} \sqrt{x}}{x^{\frac{1}{2} \cdot 2}} \cdot \sqrt{\frac{x^{2}}{8}}$

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

$\frac{\sqrt{2} \sqrt{x}}{x^{\frac{2}{2}}} \cdot \sqrt{\frac{x^{2}}{8}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{2} \sqrt{x}}{x^{\frac{2}{2}}} \cdot \sqrt{\frac{x^{2}}{8}}$

Rewrite the expression.

$\frac{\sqrt{2} \sqrt{x}}{x^{1}} \cdot \sqrt{\frac{x^{2}}{8}}$

Simplify.

$\frac{\sqrt{2} \sqrt{x}}{x} \cdot \sqrt{\frac{x^{2}}{8}}$

Combine using the product rule for radicals.

$\frac{\sqrt{2 x}}{x} \cdot \sqrt{\frac{x^{2}}{8}}$

Rewrite $\frac{x^{2}}{8}$ as ${(\frac{x}{2})}^{2} \frac{1}{2}$ .

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

$\frac{\sqrt{2 x}}{x} \cdot \sqrt{\frac{x^{2} \cdot 1}{8}}$

Factor the perfect power $2^{2}$ out of $8$ .

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

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

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

$\sqrt{\frac{1}{2}} \frac{\sqrt{2 x}}{x} \frac{x}{2}$

Rewrite $\sqrt{\frac{1}{2}}$ as $\frac{\sqrt{1}}{\sqrt{2}}$ .

$\frac{\sqrt{1}}{\sqrt{2}} \cdot \frac{\sqrt{2 x}}{x} \frac{x}{2}$

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2 x}}{x} \frac{x}{2}$

Multiply $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} \frac{\sqrt{2 x}}{x} \frac{x}{2}$

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

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

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

$\frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} \cdot \frac{\sqrt{2 x}}{x} \frac{x}{2}$

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Multiply $\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2 x}}{x}$ .

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

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

Combine using the product rule for radicals.

$\frac{\sqrt{2 (2 x)}}{2 x} \cdot \frac{x}{2}$

Multiply $2$ by $2$ .

$\frac{\sqrt{4 x}}{2 x} \cdot \frac{x}{2}$

Simplify terms.

Cancel the common factor of $x$ .

Factor $x$ out of $2 x$ .

$\frac{\sqrt{4 x}}{x \cdot 2} \cdot \frac{x}{2}$

Cancel the common factor.

$\frac{\sqrt{4 x}}{x \cdot 2} \cdot \frac{x}{2}$

Rewrite the expression.

$\frac{\sqrt{4 x}}{2} \cdot \frac{1}{2}$

Multiply $\frac{\sqrt{4 x}}{2}$ by $\frac{1}{2}$ .

$\frac{\sqrt{4 x}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{\sqrt{4 x}}{4}$

Simplify the numerator.

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

$\frac{\sqrt{2^{2} x}}{4}$

Pull terms out from under the radical.

$\frac{2 \sqrt{x}}{4}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 \sqrt{x}$ .

$\frac{2 (\sqrt{x})}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify square root of 2/x* square root of (x^2)/8

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