Trigonometry Examples

$\sqrt{410000 - 400000 \cdot \frac{\sqrt{2}}{2}}$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Factor $2$ out of $- 400000$ .

$\sqrt{410000 + 2 (- 200000) \cdot \frac{\sqrt{2}}{2}}$

Step 1.2

Cancel the common factor.

$\sqrt{410000 + 2 \cdot - 200000 \cdot \frac{\sqrt{2}}{2}}$

Step 1.3

Rewrite the expression.

$\sqrt{410000 - 200000 \cdot \sqrt{2}}$

Step 2

Rewrite $410000 - 200000 \sqrt{2}$ as $100^{2} (41 - 20 \sqrt{2})$ .

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Step 2.1

Factor $10000$ out of $410000$ .

$\sqrt{10000 (41) - 200000 \sqrt{2}}$

Step 2.2

Factor $10000$ out of $- 200000 \sqrt{2}$ .

$\sqrt{10000 (41) + 10000 (- 20 \sqrt{2})}$

Step 2.3

Factor $10000$ out of $10000 (41) + 10000 (- 20 \sqrt{2})$ .

$\sqrt{10000 (41 - 20 \sqrt{2})}$

Step 2.4

Rewrite $10000$ as $100^{2}$ .

$\sqrt{100^{2} (41 - 20 \sqrt{2})}$

Step 3

Pull terms out from under the radical.

$100 \sqrt{41 - 20 \sqrt{2}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$100 \sqrt{41 - 20 \sqrt{2}}$

Decimal Form:

$356.59120505 \dots$