Solve 1/2{1/4sqrt{frac{1/2}}}

$$\frac{ 1 }{ \frac{ 2 }{ \frac{ 1 }{ 4 } \sqrt{ \frac{ 1 }{ 2 } } } }$$

Evaluate

$$\frac{\sqrt{2}}{16}\approx 0.088388348$$

Solution Steps

Divide 1 by \frac{2}{\frac{1}{4}\sqrt{\frac{1}{2}}} by multiplying 1 by the reciprocal of \frac{2}{\frac{1}{4}\sqrt{\frac{1}{2}}}.

$$\frac{\frac{1}{4}\sqrt{\frac{1}{2}}}{2}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{\frac{1}{4}\times \frac{\sqrt{1}}{\sqrt{2}}}{2}$$

Calculate the square root of 1 and get 1.

$$\frac{\frac{1}{4}\times \frac{1}{\sqrt{2}}}{2}$$

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

$$\frac{\frac{1}{4}\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{2}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{1}{4}\times \frac{\sqrt{2}}{2}}{2}$$

Multiply \frac{1}{4} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\sqrt{2}}{4\times 2}}{2}$$

Express \frac{\frac{\sqrt{2}}{4\times 2}}{2} as a single fraction.

$$\frac{\sqrt{2}}{4\times 2\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{\sqrt{2}}{8\times 2}$$

Multiply 8 and 2 to get 16.

$$\frac{\sqrt{2}}{16}$$