Evaluate (-( square root of 2)/2)(( square root of 3)/2)

$(- \frac{\sqrt{2}}{2}) (\frac{\sqrt{3}}{2})$

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

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

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

$- \frac{\sqrt{6}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$- \frac{\sqrt{6}}{4}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{6}}{4}$

Decimal Form:

$- 0.61237243 \dots$