Solve =1/sqrt{2}*1/2div1/sqrt{2}*frac{sqrt{3}}{2}

$$= \frac { 1 } { \sqrt { 2 } } \cdot \frac { 1 } { 2 } \div \frac { 1 } { \sqrt { 2 } } \cdot \frac { \sqrt { 3 } } { 2 }$$

Evaluate

$$\frac{\sqrt{3}}{4}\approx 0.433012702$$

Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{1}{2}}{\frac{1}{\sqrt{2}}}\times \frac{\sqrt{3}}{2}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{\sqrt{2}}{2}\times \frac{1}{2}}{\frac{1}{\sqrt{2}}}\times \frac{\sqrt{3}}{2}$$

Multiply \frac{\sqrt{2}}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\sqrt{2}}{2\times 2}}{\frac{1}{\sqrt{2}}}\times \frac{\sqrt{3}}{2}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\frac{\sqrt{2}}{2\times 2}}{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}\times \frac{\sqrt{3}}{2}$$

The square of \sqrt{2} is 2.

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

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

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

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

$$\frac{1}{2}\times \frac{\sqrt{3}}{2}$$

Multiply \frac{1}{2} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{3}}{4}$$