Basic Math Examples

$6 \sqrt{18} \div 4 \sqrt{3}$

Step 1

Rewrite the division as a fraction.

$\frac{6 \sqrt{18}}{4 \sqrt{3}}$

Step 2

Cancel the common factor of $6$ and $4$ .

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Step 2.1

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

$\frac{2 (3 \sqrt{18})}{4 \sqrt{3}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\frac{2 (3 \sqrt{18})}{2 (2 \sqrt{3})}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (3 \sqrt{18})}{2 (2 \sqrt{3})}$

Step 2.2.3

Rewrite the expression.

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

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

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

Step 3

Combine $\sqrt{18}$ and $\sqrt{3}$ into a single radical.

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

Step 4

Cancel the common factor of $18$ and $3$ .

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Step 4.1

Factor $3$ out of $18$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $3$ .

$\frac{3 \sqrt{\frac{3 \cdot 6}{3 (1)}}}{2}$

Step 4.2.2

Cancel the common factor.

$\frac{3 \sqrt{\frac{3 \cdot 6}{3 \cdot 1}}}{2}$

Step 4.2.3

Rewrite the expression.

$\frac{3 \sqrt{\frac{6}{1}}}{2}$

Step 4.2.4

Divide $6$ by $1$ .

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

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.67423461 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$