Trigonometry Examples

$\sqrt{1445 - 578 \sqrt{3}}$

Step 1

Rewrite $1445 - 578 \sqrt{3}$ as $17^{2} (5 - 2 \sqrt{3})$ .

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Step 1.1

Factor $289$ out of $1445$ .

$\sqrt{289 (5) - 578 \sqrt{3}}$

Step 1.2

Factor $289$ out of $- 578 \sqrt{3}$ .

$\sqrt{289 (5) + 289 (- 2 \sqrt{3})}$

Step 1.3

Factor $289$ out of $289 (5) + 289 (- 2 \sqrt{3})$ .

$\sqrt{289 (5 - 2 \sqrt{3})}$

Step 1.4

Rewrite $289$ as $17^{2}$ .

$\sqrt{17^{2} (5 - 2 \sqrt{3})}$

Step 2

Pull terms out from under the radical.

$17 \sqrt{5 - 2 \sqrt{3}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$17 \sqrt{5 - 2 \sqrt{3}}$

Decimal Form:

$21.06833247 \dots$