Solve frac{sqrt{2}*frac{sqrt{3}}{2}}{frac{sqrt{2}}{2}}

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

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Express \sqrt{2}\times \frac{\sqrt{3}}{2} as a single fraction.

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

Divide \frac{\sqrt{2}\sqrt{3}}{2} by \frac{\sqrt{2}}{2} by multiplying \frac{\sqrt{2}\sqrt{3}}{2} by the reciprocal of \frac{\sqrt{2}}{2}.

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

Cancel out 2\sqrt{2} in both numerator and denominator.

$$\sqrt{3}$$