Basic Math Examples

4 \sqrt{189} \cdot 4 \sqrt{3}

$4 \sqrt{189} \cdot 4 \sqrt{3}$

Step 1

Rewrite

189

$189$ as

3^{2} \cdot 21

$3^{2} \cdot 21$ .

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Step 1.1

Factor

9

$9$ out of

189

$189$ .

4 \sqrt{9 (21)} \cdot (4 \sqrt{3})

$4 \sqrt{9 (21)} \cdot (4 \sqrt{3})$

Step 1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

4 \sqrt{3^{2} \cdot 21} \cdot (4 \sqrt{3})

$4 \sqrt{3^{2} \cdot 21} \cdot (4 \sqrt{3})$

4 \sqrt{3^{2} \cdot 21} \cdot (4 \sqrt{3})

$4 \sqrt{3^{2} \cdot 21} \cdot (4 \sqrt{3})$

Step 2

Pull terms out from under the radical.

4 (3 \sqrt{21}) \cdot (4 \sqrt{3})

$4 (3 \sqrt{21}) \cdot (4 \sqrt{3})$

Step 3

Multiply

3

$3$ by

4

$4$ .

12 \sqrt{21} \cdot (4 \sqrt{3})

$12 \sqrt{21} \cdot (4 \sqrt{3})$

Step 4

Multiply

12 \sqrt{21} (4 \sqrt{3})

$12 \sqrt{21} (4 \sqrt{3})$ .

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Step 4.1

Multiply

4

$4$ by

12

$12$ .

48 \sqrt{21} \sqrt{3}

$48 \sqrt{21} \sqrt{3}$

Step 4.2

Combine using the product rule for radicals.

48 \sqrt{3 \cdot 21}

$48 \sqrt{3 \cdot 21}$

Step 4.3

Multiply

3

$3$ by

21

$21$ .

48 \sqrt{63}

$48 \sqrt{63}$

48 \sqrt{63}

$48 \sqrt{63}$

Step 5

Rewrite

63

$63$ as

3^{2} \cdot 7

$3^{2} \cdot 7$ .

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Step 5.1

Factor

9

$9$ out of

63

$63$ .

48 \sqrt{9 (7)}

$48 \sqrt{9 (7)}$

Step 5.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

48 \sqrt{3^{2} \cdot 7}

$48 \sqrt{3^{2} \cdot 7}$

48 \sqrt{3^{2} \cdot 7}

$48 \sqrt{3^{2} \cdot 7}$

Step 6

Pull terms out from under the radical.

48 (3 \sqrt{7})

$48 (3 \sqrt{7})$

Step 7

Multiply

3

$3$ by

48

$48$ .

144 \sqrt{7}

$144 \sqrt{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

144 \sqrt{7}

$144 \sqrt{7}$

Decimal Form:

380.98818879 \dots

$380.98818879 \dots$

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

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