Solve sqrt{2/10}*sqrt{8/90}=

$$\sqrt { \frac { 2 } { 10 } } \cdot \sqrt { \frac { 8 } { 90 } } =$$

Evaluate

$$\frac{2}{15}\approx 0.133333333$$

Solution Steps

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

$$\sqrt{\frac{1}{5}}\sqrt{\frac{8}{90}}$$

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$\frac{\sqrt{1}}{\sqrt{5}}\sqrt{\frac{8}{90}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{5}}\sqrt{\frac{8}{90}}$$

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{\frac{8}{90}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{5}\sqrt{\frac{8}{90}}$$

Reduce the fraction \frac{8}{90} to lowest terms by extracting and canceling out 2.

$$\frac{\sqrt{5}}{5}\sqrt{\frac{4}{45}}$$

Rewrite the square root of the division \sqrt{\frac{4}{45}} as the division of square roots \frac{\sqrt{4}}{\sqrt{45}}.

$$\frac{\sqrt{5}}{5}\times \frac{\sqrt{4}}{\sqrt{45}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{5}}{5}\times \frac{2}{\sqrt{45}}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{\sqrt{5}}{5}\times \frac{2}{3\sqrt{5}}$$

Rationalize the denominator of \frac{2}{3\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{5}\times \frac{2\sqrt{5}}{3\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{5}\times \frac{2\sqrt{5}}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{\sqrt{5}}{5}\times \frac{2\sqrt{5}}{15}$$

Multiply \frac{\sqrt{5}}{5} times \frac{2\sqrt{5}}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{5}\times 2\sqrt{5}}{5\times 15}$$

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

$$\frac{5\times 2}{5\times 15}$$

Cancel out 5 in both numerator and denominator.

$$\frac{2}{15}$$

Factor

$$\frac{2}{3 \cdot 5} = 0.13333333333333333$$