Simplify (3 square root of 2)/2+ square root of 2

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

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

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

Combine fractions.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

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

Add $3 \sqrt{2}$ and $2 \sqrt{2}$ .

$\frac{5 \sqrt{2}}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{2}}{2}$

Decimal Form:

$3.53553390 \dots$