Algebra Examples

$\sqrt{2} - \frac{\sqrt{2}}{2}$

Step 1

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

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

Step 2

Combine fractions.

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Step 2.1

Combine $\sqrt{2}$ and $\frac{2}{2}$ .

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

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Step 3.1

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

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

Step 3.2

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

$\frac{\sqrt{2}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{2}}{2}$

Decimal Form:

$0.70710678 \dots$