Trigonometry Examples

$6 \sqrt{128} - \sqrt{32} + 8 \sqrt{162}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $64$ out of $128$ .

$6 \sqrt{64 (2)} - \sqrt{32} + 8 \sqrt{162}$

Step 1.1.2

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

$6 \sqrt{8^{2} \cdot 2} - \sqrt{32} + 8 \sqrt{162}$

Step 1.2

Pull terms out from under the radical.

$6 (8 \sqrt{2}) - \sqrt{32} + 8 \sqrt{162}$

Step 1.3

Multiply $8$ by $6$ .

$48 \sqrt{2} - \sqrt{32} + 8 \sqrt{162}$

Step 1.4

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.4.1

Factor $16$ out of $32$ .

$48 \sqrt{2} - \sqrt{16 (2)} + 8 \sqrt{162}$

Step 1.4.2

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

$48 \sqrt{2} - \sqrt{4^{2} \cdot 2} + 8 \sqrt{162}$

Step 1.5

Pull terms out from under the radical.

$48 \sqrt{2} - (4 \sqrt{2}) + 8 \sqrt{162}$

Step 1.6

Multiply $4$ by $- 1$ .

$48 \sqrt{2} - 4 \sqrt{2} + 8 \sqrt{162}$

Step 1.7

Rewrite $162$ as $9^{2} \cdot 2$ .

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Step 1.7.1

Factor $81$ out of $162$ .

$48 \sqrt{2} - 4 \sqrt{2} + 8 \sqrt{81 (2)}$

Step 1.7.2

Rewrite $81$ as $9^{2}$ .

$48 \sqrt{2} - 4 \sqrt{2} + 8 \sqrt{9^{2} \cdot 2}$

Step 1.8

Pull terms out from under the radical.

$48 \sqrt{2} - 4 \sqrt{2} + 8 (9 \sqrt{2})$

Step 1.9

Multiply $9$ by $8$ .

$48 \sqrt{2} - 4 \sqrt{2} + 72 \sqrt{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $4 \sqrt{2}$ from $48 \sqrt{2}$ .

$44 \sqrt{2} + 72 \sqrt{2}$

Step 2.2

Add $44 \sqrt{2}$ and $72 \sqrt{2}$ .

$116 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$116 \sqrt{2}$

Decimal Form:

$164.04877323 \dots$