Solve 1divsqrt{1/2}

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

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

$$\sqrt{2}$$