Basic Math Examples

$\sqrt{3 - \sqrt{2}} \div \sqrt{3 + \sqrt{2} \cdot 2} - 22 \sqrt{4}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$\frac{\sqrt{3 - \sqrt{2}}}{\sqrt{3 + \sqrt{2} \cdot 2}} - 22 \sqrt{4}$

Step 1.2

Move $2$ to the left of $\sqrt{2}$ .

$\frac{\sqrt{3 - \sqrt{2}}}{\sqrt{3 + 2 \sqrt{2}}} - 22 \sqrt{4}$

Step 1.3

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

$\frac{\sqrt{3 - \sqrt{2}}}{\sqrt{3 + 2 \sqrt{2}}} - 22 \sqrt{2^{2}}$

Step 1.4

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

$\frac{\sqrt{3 - \sqrt{2}}}{\sqrt{3 + 2 \sqrt{2}}} - 22 \cdot 2$

Step 1.5

Multiply $- 22$ by $2$ .

$\frac{\sqrt{3 - \sqrt{2}}}{\sqrt{3 + 2 \sqrt{2}}} - 44$

Step 2

To write $- 44$ as a fraction with a common denominator, multiply by $\frac{\sqrt{3 + 2 \sqrt{2}}}{\sqrt{3 + 2 \sqrt{2}}}$ .

$\frac{\sqrt{3 - \sqrt{2}}}{\sqrt{3 + 2 \sqrt{2}}} - 44 \cdot \frac{\sqrt{3 + 2 \sqrt{2}}}{\sqrt{3 + 2 \sqrt{2}}}$

Step 3

Combine $- 44$ and $\frac{\sqrt{3 + 2 \sqrt{2}}}{\sqrt{3 + 2 \sqrt{2}}}$ .

$\frac{\sqrt{3 - \sqrt{2}}}{\sqrt{3 + 2 \sqrt{2}}} + \frac{- 44 \sqrt{3 + 2 \sqrt{2}}}{\sqrt{3 + 2 \sqrt{2}}}$

Step 4

Combine the numerators over the common denominator.

$\frac{\sqrt{3 - \sqrt{2}} - 44 \sqrt{3 + 2 \sqrt{2}}}{\sqrt{3 + 2 \sqrt{2}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3 - \sqrt{2}} - 44 \sqrt{3 + 2 \sqrt{2}}}{\sqrt{3 + 2 \sqrt{2}}}$

Decimal Form:

$- 43.47838909 \dots$