Solve 1sqrt{4/5}

$$1 \sqrt { \frac { 4 } { 5 } }$$

Evaluate

$$\frac{2\sqrt{5}}{5}\approx 0.894427191$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{4}{5}} as the division of square roots \frac{\sqrt{4}}{\sqrt{5}}.

$$1\times \frac{\sqrt{4}}{\sqrt{5}}$$

Calculate the square root of 4 and get 2.

$$1\times \frac{2}{\sqrt{5}}$$

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

$$1\times \frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$1\times \frac{2\sqrt{5}}{5}$$

Express 1\times \frac{2\sqrt{5}}{5} as a single fraction.

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