Trigonometry Examples

$\sqrt{128 - 64 \sqrt{3}}$

Step 1

Rewrite $128 - 64 \sqrt{3}$ as $8^{2} (2 - \sqrt{3})$ .

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Step 1.1

Factor $64$ out of $128$ .

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

Step 1.2

Factor $64$ out of $- 64 \sqrt{3}$ .

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

Step 1.3

Factor $64$ out of $64 (2) + 64 (- \sqrt{3})$ .

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

Step 1.4

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$4.14110472 \dots$