Evaluate (( square root of 2)/2)(( square root of 3)/2)+(( square root of 2)/2)(1/2)

$(\frac{\sqrt{2}}{2}) (\frac{\sqrt{3}}{2}) + (\frac{\sqrt{2}}{2}) (\frac{1}{2})$

Simplify each term.

Multiply $(\frac{\sqrt{2}}{2}) (\frac{\sqrt{3}}{2})$ .

Multiply $\frac{\sqrt{2}}{2}$ by $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{2} \sqrt{3}}{2 \cdot 2} + (\frac{\sqrt{2}}{2}) (\frac{1}{2})$

Combine using the product rule for radicals.

$\frac{\sqrt{2 \cdot 3}}{2 \cdot 2} + (\frac{\sqrt{2}}{2}) (\frac{1}{2})$

Multiply $2$ by $3$ .

$\frac{\sqrt{6}}{2 \cdot 2} + (\frac{\sqrt{2}}{2}) (\frac{1}{2})$

Multiply $2$ by $2$ .

$\frac{\sqrt{6}}{4} + (\frac{\sqrt{2}}{2}) (\frac{1}{2})$

Multiply $(\frac{\sqrt{2}}{2}) (\frac{1}{2})$ .

Multiply $\frac{\sqrt{2}}{2}$ by $\frac{1}{2}$ .

$\frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}$

Combine the numerators over the common denominator.

$\frac{\sqrt{6} + \sqrt{2}}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{6} + \sqrt{2}}{4}$

Decimal Form:

$0.96592582 \dots$