Solve sqrt{2/5}*sqrt{10/8}

$$\sqrt { \frac { 2 } { 5 } } \cdot \sqrt { \frac { 10 } { 8 } }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

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

$$\frac{\sqrt{2}}{\sqrt{5}}\sqrt{\frac{10}{8}}$$

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

$$\frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{\frac{10}{8}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{2}\sqrt{5}}{5}\sqrt{\frac{10}{8}}$$

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

$$\frac{\sqrt{10}}{5}\sqrt{\frac{10}{8}}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{\sqrt{10}}{5}\sqrt{\frac{5}{4}}$$

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

$$\frac{\sqrt{10}}{5}\times \frac{\sqrt{5}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

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

Multiply \frac{\sqrt{10}}{5} times \frac{\sqrt{5}}{2} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Multiply 5 and 2 to get 10.

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

Divide 5\sqrt{2} by 10 to get \frac{1}{2}\sqrt{2}.

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