Basic Math Examples

$\frac{18 \sqrt{2}}{6 \sqrt{3}}$

Step 1

Cancel the common factor of $18$ and $6$ .

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Step 1.1

Factor $6$ out of $18 \sqrt{2}$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $6$ out of $6 \sqrt{3}$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

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

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

Step 3

Combine and simplify the denominator.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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

Step 3.5

Add $1$ and $1$ .

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

Step 3.6

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

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Step 3.6.1

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

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

Step 3.6.2

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

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

Step 3.6.3

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

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

Step 3.6.4

Cancel the common factor of $2$ .

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Step 3.6.4.1

Cancel the common factor.

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

Step 3.6.4.2

Rewrite the expression.

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

Step 3.6.5

Evaluate the exponent.

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

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $\sqrt{2} \sqrt{3}$ by $1$ .

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

Step 5

Combine using the product rule for radicals.

$\sqrt{2 \cdot 3}$

Step 6

Multiply $2$ by $3$ .

$\sqrt{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt{6}$

Decimal Form:

$2.44948974 \dots$