Basic Math Examples

$\frac{1}{6} \cdot \frac{3}{2} \cdot (\sqrt{26} \sqrt{72})$

Step 1

Cancel the common factor of $3$ .

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Step 1.1

Factor $3$ out of $6$ .

$\frac{1}{3 (2)} \cdot \frac{3}{2} \cdot (\sqrt{26} \sqrt{72})$

Step 1.2

Cancel the common factor.

$\frac{1}{3 \cdot 2} \cdot \frac{3}{2} \cdot (\sqrt{26} \sqrt{72})$

Step 1.3

Rewrite the expression.

$\frac{1}{2} \cdot \frac{1}{2} \cdot (\sqrt{26} \sqrt{72})$

Step 2

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

$\frac{1}{2 \cdot 2} \cdot (\sqrt{26} \sqrt{72})$

Step 3

Multiply $2$ by $2$ .

$\frac{1}{4} \cdot (\sqrt{26} \sqrt{72})$

Step 4

Combine using the product rule for radicals.

$\frac{1}{4} \cdot \sqrt{26 \cdot 72}$

Step 5

Multiply $26$ by $72$ .

$\frac{1}{4} \cdot \sqrt{1872}$

Step 6

Rewrite $1872$ as $12^{2} \cdot 13$ .

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Step 6.1

Factor $144$ out of $1872$ .

$\frac{1}{4} \cdot \sqrt{144 (13)}$

Step 6.2

Rewrite $144$ as $12^{2}$ .

$\frac{1}{4} \cdot \sqrt{12^{2} \cdot 13}$

Step 7

Pull terms out from under the radical.

$\frac{1}{4} \cdot (12 \sqrt{13})$

Step 8

Cancel the common factor of $4$ .

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Step 8.1

Factor $4$ out of $12 \sqrt{13}$ .

$\frac{1}{4} \cdot (4 (3 \sqrt{13}))$

Step 8.2

Cancel the common factor.

$\frac{1}{4} \cdot (4 (3 \sqrt{13}))$

Step 8.3

Rewrite the expression.

$3 \sqrt{13}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{13}$

Decimal Form:

$10.81665382 \dots$