Simplify (2 square root of 8x)/(3 square root of 6)

$\frac{2 \sqrt{8 x}}{3 \sqrt{6}}$

Combine $\sqrt{8 x}$ and $\sqrt{6}$ into a single radical.

$\frac{2 \sqrt{\frac{8 x}{6}}}{3}$

Cancel the common factor of $8$ and $6$ .

Factor $2$ out of $8 x$ .

$\frac{2 \sqrt{\frac{2 (4 x)}{6}}}{3}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 \sqrt{\frac{2 (4 x)}{2 (3)}}}{3}$

Cancel the common factor.

$\frac{2 \sqrt{\frac{2 (4 x)}{2 \cdot 3}}}{3}$

Rewrite the expression.

$\frac{2 \sqrt{\frac{4 x}{3}}}{3}$

Simplify the numerator.

Rewrite $\sqrt{\frac{4 x}{3}}$ as $\frac{\sqrt{4 x}}{\sqrt{3}}$ .

$\frac{2 \frac{\sqrt{4 x}}{\sqrt{3}}}{3}$

Simplify the numerator.

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

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

Pull terms out from under the radical.

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

Multiply $\frac{2 \sqrt{x}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{2 \sqrt{x}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

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

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

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

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

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

$\frac{2 \frac{2 \sqrt{x} \sqrt{3}}{{\sqrt{3}}^{1 + 1}}}{3}$

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Combine using the product rule for radicals.

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

Combine $2$ and $\frac{2 \sqrt{3 x}}{3}$ .

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

Multiply $2$ by $2$ .

$\frac{\frac{4 \sqrt{3 x}}{3}}{3}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{4 \sqrt{3 x}}{3} \cdot \frac{1}{3}$

Multiply $\frac{4 \sqrt{3 x}}{3} \cdot \frac{1}{3}$ .

Multiply $\frac{4 \sqrt{3 x}}{3}$ by $\frac{1}{3}$ .

$\frac{4 \sqrt{3 x}}{3 \cdot 3}$

Multiply $3$ by $3$ .

$\frac{4 \sqrt{3 x}}{9}$

Simplify (2 square root of 8x)/(3 square root of 6)

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