Algebra Examples

$2 \sqrt{2} \div 4 \sqrt{3}$

Step 1

Rewrite the division as a fraction.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $4 \sqrt{3}$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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Step 4.1

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

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

Step 4.2

Move $\sqrt{3}$ .

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

Step 4.3

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

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

Step 4.4

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

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

Step 4.5

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

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

Step 4.6

Add $1$ and $1$ .

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

Step 4.7

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

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Step 4.7.1

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

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

Step 4.7.2

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

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

Step 4.7.3

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

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

Step 4.7.4

Cancel the common factor of $2$ .

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Step 4.7.4.1

Cancel the common factor.

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

Step 4.7.4.2

Rewrite the expression.

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

Step 4.7.5

Evaluate the exponent.

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

Step 5

Simplify the numerator.

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Step 5.1

Combine using the product rule for radicals.

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

Step 5.2

Multiply $2$ by $3$ .

$\frac{\sqrt{6}}{2 \cdot 3}$

Step 6

Multiply $2$ by $3$ .

$\frac{\sqrt{6}}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{6}}{6}$

Decimal Form:

$0.40824829 \dots$