Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Factor $2$ out of $8 x$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $6$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Simplify the numerator.

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Step 3.1

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

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

Step 3.2

Simplify the numerator.

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Step 3.2.1

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

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

Step 3.2.2

Pull terms out from under the radical.

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

Step 3.3

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

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

Step 3.4

Combine and simplify the denominator.

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Step 3.4.1

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

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

Step 3.4.2

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

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

Step 3.4.3

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

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

Step 3.4.4

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

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

Step 3.4.5

Add $1$ and $1$ .

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

Step 3.4.6

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

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Step 3.4.6.1

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

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

Step 3.4.6.2

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

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

Step 3.4.6.3

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

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

Step 3.4.6.4

Cancel the common factor of $2$ .

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Step 3.4.6.4.1

Cancel the common factor.

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

Step 3.4.6.4.2

Rewrite the expression.

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

Step 3.4.6.5

Evaluate the exponent.

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

Step 3.5

Combine using the product rule for radicals.

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

Step 4

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

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

Step 5

Multiply $2$ by $2$ .

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

Step 6

Multiply the numerator by the reciprocal of the denominator.

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Multiply $3$ by $3$ .

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