Solve sqrt{3/20}*sqrt{22/5}

$$\sqrt { \frac { 3 } { 20 } } \times \sqrt { 2 \frac { 2 } { 5 } }$$

Evaluate

$$\frac{3}{5}=0.6$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{20}} as the division of square roots \frac{\sqrt{3}}{\sqrt{20}}.

$$\frac{\sqrt{3}}{\sqrt{20}}\sqrt{\frac{2\times 5+2}{5}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

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

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

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

The square of \sqrt{5} is 5.

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

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

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

Multiply 2 and 5 to get 10.

$$\frac{\sqrt{15}}{10}\sqrt{\frac{2\times 5+2}{5}}$$

Multiply 2 and 5 to get 10.

$$\frac{\sqrt{15}}{10}\sqrt{\frac{10+2}{5}}$$

Add 10 and 2 to get 12.

$$\frac{\sqrt{15}}{10}\sqrt{\frac{12}{5}}$$

Rewrite the square root of the division \sqrt{\frac{12}{5}} as the division of square roots \frac{\sqrt{12}}{\sqrt{5}}.

$$\frac{\sqrt{15}}{10}\times \frac{\sqrt{12}}{\sqrt{5}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{\sqrt{15}}{10}\times \frac{2\sqrt{3}}{\sqrt{5}}$$

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

$$\frac{\sqrt{15}}{10}\times \frac{2\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{15}}{10}\times \frac{2\sqrt{3}\sqrt{5}}{5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{15}}{10}\times \frac{2\sqrt{15}}{5}$$

Multiply \frac{\sqrt{15}}{10} times \frac{2\sqrt{15}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{15}\times 2\sqrt{15}}{10\times 5}$$

Cancel out 2 in both numerator and denominator.

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

Multiply \sqrt{15} and \sqrt{15} to get 15.

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

Multiply 5 and 5 to get 25.

$$\frac{15}{25}$$

Reduce the fraction \frac{15}{25} to lowest terms by extracting and canceling out 5.

$$\frac{3}{5}$$

Factor

$$\frac{3}{5} = 0.6$$