Solve 4/5sqrt{5/4}

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

Evaluate

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

Solution Steps

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

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

Calculate the square root of 4 and get 2.

$$\frac{4}{5}\times \frac{\sqrt{5}}{2}$$

Multiply \frac{4}{5} times \frac{\sqrt{5}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\sqrt{5}}{5\times 2}$$

Cancel out 2 in both numerator and denominator.

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