Simplify square root of 6/x* square root of (x^2)/24

$\sqrt{\frac{6}{x}} \cdot \sqrt{\frac{x^{2}}{24}}$

Rewrite $\sqrt{\frac{6}{x}}$ as $\frac{\sqrt{6}}{\sqrt{x}}$ .

$\frac{\sqrt{6}}{\sqrt{x}} \cdot \sqrt{\frac{x^{2}}{24}}$

Multiply $\frac{\sqrt{6}}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{\sqrt{6}}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}} \cdot \sqrt{\frac{x^{2}}{24}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{6}}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{\sqrt{6} \sqrt{x}}{\sqrt{x} \sqrt{x}} \cdot \sqrt{\frac{x^{2}}{24}}$

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

$\frac{\sqrt{6} \sqrt{x}}{{\sqrt{x}}^{1} \sqrt{x}} \cdot \sqrt{\frac{x^{2}}{24}}$

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

$\frac{\sqrt{6} \sqrt{x}}{{\sqrt{x}}^{1} {\sqrt{x}}^{1}} \cdot \sqrt{\frac{x^{2}}{24}}$

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

$\frac{\sqrt{6} \sqrt{x}}{{\sqrt{x}}^{1 + 1}} \cdot \sqrt{\frac{x^{2}}{24}}$

Add $1$ and $1$ .

$\frac{\sqrt{6} \sqrt{x}}{{\sqrt{x}}^{2}} \cdot \sqrt{\frac{x^{2}}{24}}$

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

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

$\frac{\sqrt{6} \sqrt{x}}{{(x^{\frac{1}{2}})}^{2}} \cdot \sqrt{\frac{x^{2}}{24}}$

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

$\frac{\sqrt{6} \sqrt{x}}{x^{\frac{1}{2} \cdot 2}} \cdot \sqrt{\frac{x^{2}}{24}}$

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

$\frac{\sqrt{6} \sqrt{x}}{x^{\frac{2}{2}}} \cdot \sqrt{\frac{x^{2}}{24}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{6} \sqrt{x}}{x^{\frac{2}{2}}} \cdot \sqrt{\frac{x^{2}}{24}}$

Rewrite the expression.

$\frac{\sqrt{6} \sqrt{x}}{x^{1}} \cdot \sqrt{\frac{x^{2}}{24}}$

Simplify.

$\frac{\sqrt{6} \sqrt{x}}{x} \cdot \sqrt{\frac{x^{2}}{24}}$

Combine using the product rule for radicals.

$\frac{\sqrt{6 x}}{x} \cdot \sqrt{\frac{x^{2}}{24}}$

Rewrite $\frac{x^{2}}{24}$ as ${(\frac{x}{2})}^{2} \frac{1}{6}$ .

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

$\frac{\sqrt{6 x}}{x} \cdot \sqrt{\frac{x^{2} \cdot 1}{24}}$

Factor the perfect power $2^{2}$ out of $24$ .

$\frac{\sqrt{6 x}}{x} \cdot \sqrt{\frac{x^{2} \cdot 1}{2^{2} \cdot 6}}$

Rearrange the fraction $\frac{x^{2} \cdot 1}{2^{2} \cdot 6}$ .

$\frac{\sqrt{6 x}}{x} \cdot \sqrt{{(\frac{x}{2})}^{2} \frac{1}{6}}$

Pull terms out from under the radical.

$\frac{\sqrt{6 x}}{x} \cdot (\frac{x}{2} \sqrt{\frac{1}{6}})$

Rewrite using the commutative property of multiplication.

$\sqrt{\frac{1}{6}} \frac{\sqrt{6 x}}{x} \frac{x}{2}$

Rewrite $\sqrt{\frac{1}{6}}$ as $\frac{\sqrt{1}}{\sqrt{6}}$ .

$\frac{\sqrt{1}}{\sqrt{6}} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{6}} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

Multiply $\frac{1}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{1}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}} \frac{\sqrt{6 x}}{x} \frac{x}{2}$

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{\sqrt{6}}{\sqrt{6} \sqrt{6}} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{\sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{\sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

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

$\frac{\sqrt{6}}{{\sqrt{6}}^{1 + 1}} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

Add $1$ and $1$ .

$\frac{\sqrt{6}}{{\sqrt{6}}^{2}} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$\frac{\sqrt{6}}{{(6^{\frac{1}{2}})}^{2}} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

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

$\frac{\sqrt{6}}{6^{\frac{1}{2} \cdot 2}} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

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

$\frac{\sqrt{6}}{6^{\frac{2}{2}}} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{6}}{6^{\frac{2}{2}}} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

Rewrite the expression.

$\frac{\sqrt{6}}{6^{1}} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

Evaluate the exponent.

$\frac{\sqrt{6}}{6} \cdot \frac{\sqrt{6 x}}{x} \frac{x}{2}$

Multiply $\frac{\sqrt{6}}{6} \cdot \frac{\sqrt{6 x}}{x}$ .

Multiply $\frac{\sqrt{6}}{6}$ by $\frac{\sqrt{6 x}}{x}$ .

$\frac{\sqrt{6} \sqrt{6 x}}{6 x} \cdot \frac{x}{2}$

Combine using the product rule for radicals.

$\frac{\sqrt{6 (6 x)}}{6 x} \cdot \frac{x}{2}$

Multiply $6$ by $6$ .

$\frac{\sqrt{36 x}}{6 x} \cdot \frac{x}{2}$

Simplify terms.

Cancel the common factor of $x$ .

Factor $x$ out of $6 x$ .

$\frac{\sqrt{36 x}}{x \cdot 6} \cdot \frac{x}{2}$

Cancel the common factor.

$\frac{\sqrt{36 x}}{x \cdot 6} \cdot \frac{x}{2}$

Rewrite the expression.

$\frac{\sqrt{36 x}}{6} \cdot \frac{1}{2}$

Multiply $\frac{\sqrt{36 x}}{6}$ by $\frac{1}{2}$ .

$\frac{\sqrt{36 x}}{6 \cdot 2}$

Multiply $6$ by $2$ .

$\frac{\sqrt{36 x}}{12}$

Simplify the numerator.

Rewrite $36$ as $6^{2}$ .

$\frac{\sqrt{6^{2} x}}{12}$

Pull terms out from under the radical.

$\frac{6 \sqrt{x}}{12}$

Cancel the common factor of $6$ and $12$ .

Factor $6$ out of $6 \sqrt{x}$ .

$\frac{6 (\sqrt{x})}{12}$

Cancel the common factors.

Factor $6$ out of $12$ .

$\frac{6 \sqrt{x}}{6 \cdot 2}$

Cancel the common factor.

$\frac{6 \sqrt{x}}{6 \cdot 2}$

Rewrite the expression.

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

Simplify square root of 6/x* square root of (x^2)/24

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