Basic Math Examples

$\sqrt{12} - \sqrt{192}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

$12$ as

$2^{2} \cdot 3$ .

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Step 1.1.1

Factor

$4$ out of

$12$ .

$\sqrt{4 (3)} - \sqrt{192}$

Step 1.1.2

Rewrite

$4$ as

$2^{2}$ .

$\sqrt{2^{2} \cdot 3} - \sqrt{192}$

$\sqrt{2^{2} \cdot 3} - \sqrt{192}$

Step 1.2

Pull terms out from under the radical.

$2 \sqrt{3} - \sqrt{192}$

Step 1.3

Rewrite

$192$ as

$8^{2} \cdot 3$ .

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Step 1.3.1

Factor

$64$ out of

$192$ .

$2 \sqrt{3} - \sqrt{64 (3)}$

Step 1.3.2

Rewrite

$64$ as

$8^{2}$ .

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

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

Step 1.4

Pull terms out from under the radical.

$2 \sqrt{3} - (8 \sqrt{3})$

Step 1.5

Multiply

$8$ by

$- 1$ .

$2 \sqrt{3} - 8 \sqrt{3}$

$2 \sqrt{3} - 8 \sqrt{3}$

Step 2

Subtract

$8 \sqrt{3}$ from

$2 \sqrt{3}$ .

$- 6 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 6 \sqrt{3}$

Decimal Form:

$- 10.39230484 \dots$

Enter a problem...

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