Basic Math Examples

\sqrt{32} \cdot \sqrt{6}

$\sqrt{32} \cdot \sqrt{6}$

Step 1

Combine using the product rule for radicals.

\sqrt{32 \cdot 6}

$\sqrt{32 \cdot 6}$

Step 2

Multiply

32

$32$ by

6

$6$ .

\sqrt{192}

$\sqrt{192}$

Step 3

Rewrite

192

$192$ as

8^{2} \cdot 3

$8^{2} \cdot 3$ .

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Step 3.1

Factor

64

$64$ out of

192

$192$ .

\sqrt{64 (3)}

$\sqrt{64 (3)}$

Step 3.2

Rewrite

64

$64$ as

8^{2}

$8^{2}$ .

\sqrt{8^{2} \cdot 3}

$\sqrt{8^{2} \cdot 3}$

\sqrt{8^{2} \cdot 3}

$\sqrt{8^{2} \cdot 3}$

Step 4

Pull terms out from under the radical.

8 \sqrt{3}

$8 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

8 \sqrt{3}

$8 \sqrt{3}$

Decimal Form:

13.85640646 \dots

$13.85640646 \dots$

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

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