Basic Math Examples

\sqrt{12} - \sqrt{192}

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

Step 1

Simplify each term.

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Step 1.1

Rewrite

12

$12$ as

2^{2} \cdot 3

$2^{2} \cdot 3$ .

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Step 1.1.1

Factor

4

$4$ out of

12

$12$ .

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

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

Step 1.1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

\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}

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

Step 1.3

Rewrite

192

$192$ as

8^{2} \cdot 3

$8^{2} \cdot 3$ .

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Step 1.3.1

Factor

64

$64$ out of

192

$192$ .

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

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

Step 1.3.2

Rewrite

64

$64$ as

8^{2}

$8^{2}$ .

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

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

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})

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

Step 1.5

Multiply

8

$8$ by

- 1

$- 1$ .

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

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

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

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

Step 2

Subtract

8 \sqrt{3}

$8 \sqrt{3}$ from

2 \sqrt{3}

$2 \sqrt{3}$ .

- 6 \sqrt{3}

$- 6 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

- 6 \sqrt{3}

$- 6 \sqrt{3}$

Decimal Form:

- 10.39230484 \dots

$- 10.39230484 \dots$

\sqrt[]{12} - \sqrt[]{192}

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

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

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