Basic Math Examples

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

Step 1

Rewrite $54$ as $3^{2} \cdot 6$ .

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Step 1.1

Factor $9$ out of $54$ .

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

Step 1.2

Rewrite $9$ as $3^{2}$ .

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite $16$ as $4^{2}$ .

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

Step 4

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

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

Step 5

Multiply $- 1$ by $4$ .

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

Step 6

Rewrite $128$ as $8^{2} \cdot 2$ .

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Step 6.1

Factor $64$ out of $128$ .

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

Step 6.2

Rewrite $64$ as $8^{2}$ .

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

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

Step 7

Pull terms out from under the radical.

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

Step 8

Multiply $8$ by $- 1$ .

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

Step 9

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 7.96523927 \dots$

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