Basic Math Examples

\sqrt{54} - \sqrt{16} - \sqrt{128}

$\sqrt{54} - \sqrt{16} - \sqrt{128}$

Step 1

Rewrite

54

$54$ as

3^{2} \cdot 6

$3^{2} \cdot 6$ .

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Step 1.1

Factor

9

$9$ out of

54

$54$ .

\sqrt{9 (6)} - \sqrt{16} - \sqrt{128}

$\sqrt{9 (6)} - \sqrt{16} - \sqrt{128}$

Step 1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

\sqrt{3^{2} \cdot 6} - \sqrt{16} - \sqrt{128}

$\sqrt{3^{2} \cdot 6} - \sqrt{16} - \sqrt{128}$

\sqrt{3^{2} \cdot 6} - \sqrt{16} - \sqrt{128}

$\sqrt{3^{2} \cdot 6} - \sqrt{16} - \sqrt{128}$

Step 2

Pull terms out from under the radical.

3 \sqrt{6} - \sqrt{16} - \sqrt{128}

$3 \sqrt{6} - \sqrt{16} - \sqrt{128}$

Step 3

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

3 \sqrt{6} - \sqrt{4^{2}} - \sqrt{128}

$3 \sqrt{6} - \sqrt{4^{2}} - \sqrt{128}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

3 \sqrt{6} - 1 \cdot 4 - \sqrt{128}

$3 \sqrt{6} - 1 \cdot 4 - \sqrt{128}$

Step 5

Multiply

- 1

$- 1$ by

4

$4$ .

3 \sqrt{6} - 4 - \sqrt{128}

$3 \sqrt{6} - 4 - \sqrt{128}$

Step 6

Rewrite

128

$128$ as

8^{2} \cdot 2

$8^{2} \cdot 2$ .

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Step 6.1

Factor

64

$64$ out of

128

$128$ .

3 \sqrt{6} - 4 - \sqrt{64 (2)}

$3 \sqrt{6} - 4 - \sqrt{64 (2)}$

Step 6.2

Rewrite

64

$64$ as

8^{2}

$8^{2}$ .

3 \sqrt{6} - 4 - \sqrt{8^{2} \cdot 2}

$3 \sqrt{6} - 4 - \sqrt{8^{2} \cdot 2}$

3 \sqrt{6} - 4 - \sqrt{8^{2} \cdot 2}

$3 \sqrt{6} - 4 - \sqrt{8^{2} \cdot 2}$

Step 7

Pull terms out from under the radical.

3 \sqrt{6} - 4 - (8 \sqrt{2})

$3 \sqrt{6} - 4 - (8 \sqrt{2})$

Step 8

Multiply

8

$8$ by

- 1

$- 1$ .

3 \sqrt{6} - 4 - 8 \sqrt{2}

$3 \sqrt{6} - 4 - 8 \sqrt{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

3 \sqrt{6} - 4 - 8 \sqrt{2}

$3 \sqrt{6} - 4 - 8 \sqrt{2}$

Decimal Form:

- 7.96523927 \dots

$- 7.96523927 \dots$

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

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