Basic Math Examples

4 \sqrt{3} \cdot 3 \sqrt{18}

$4 \sqrt{3} \cdot 3 \sqrt{18}$

Step 1

Rewrite

18

$18$ as

3^{2} \cdot 2

$3^{2} \cdot 2$ .

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Step 1.1

Factor

9

$9$ out of

18

$18$ .

4 \sqrt{3} \cdot (3 \sqrt{9 (2)})

$4 \sqrt{3} \cdot (3 \sqrt{9 (2)})$

Step 1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

4 \sqrt{3} \cdot (3 \sqrt{3^{2} \cdot 2})

$4 \sqrt{3} \cdot (3 \sqrt{3^{2} \cdot 2})$

4 \sqrt{3} \cdot (3 \sqrt{3^{2} \cdot 2})

$4 \sqrt{3} \cdot (3 \sqrt{3^{2} \cdot 2})$

Step 2

Pull terms out from under the radical.

4 \sqrt{3} \cdot (3 (3 \sqrt{2}))

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

Step 3

Multiply

3

$3$ by

3

$3$ .

4 \sqrt{3} \cdot (9 \sqrt{2})

$4 \sqrt{3} \cdot (9 \sqrt{2})$

Step 4

Multiply

4 \sqrt{3} (9 \sqrt{2})

$4 \sqrt{3} (9 \sqrt{2})$ .

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Step 4.1

Multiply

9

$9$ by

4

$4$ .

36 \sqrt{3} \sqrt{2}

$36 \sqrt{3} \sqrt{2}$

Step 4.2

Combine using the product rule for radicals.

36 \sqrt{2 \cdot 3}

$36 \sqrt{2 \cdot 3}$

Step 4.3

Multiply

2

$2$ by

3

$3$ .

36 \sqrt{6}

$36 \sqrt{6}$

36 \sqrt{6}

$36 \sqrt{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

36 \sqrt{6}

$36 \sqrt{6}$

Decimal Form:

88.18163074 \dots

$88.18163074 \dots$

$4 \sqrt[]{3} \cdot 3 \sqrt[]{18}$

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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