Solve sqrt{1/0.4}

$$\sqrt{ \frac{ 1 }{ 0.4 } }$$

Evaluate

$$\frac{\sqrt{10}}{2}\approx 1.58113883$$

Solution Steps

Expand \frac{1}{0.4} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{10}{4}}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{5}{2}}$$

Rewrite the square root of the division \sqrt{\frac{5}{2}} as the division of square roots \frac{\sqrt{5}}{\sqrt{2}}.

$$\frac{\sqrt{5}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{5}\sqrt{2}}{2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{10}}{2}$$