Solve frac{sqrt{10}}{5/2sqrt{2}}

$$\frac { \sqrt { 10 } } { \frac { 5 } { 2 } \sqrt { 2 } }$$

Evaluate

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

Solution Steps

Rationalize the denominator of \frac{\sqrt{10}}{\frac{5}{2}\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{10}\sqrt{2}}{\frac{5}{2}\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{10}\sqrt{2}}{\frac{5}{2}\times 2}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Cancel out 2 and 2.

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