Solve sqrt{13/5}div22sqrt{1/5}*sqrt{63}=

$$\sqrt { 1 \frac { 3 } { 5 } } \div 22 \sqrt { \frac { 1 } { 5 } } \times \sqrt { 63 } =$$

Evaluate

$$\frac{3\sqrt{14}}{55}\approx 0.204090403$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\frac{\sqrt{\frac{5+3}{5}}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

Add 5 and 3 to get 8.

$$\frac{\sqrt{\frac{8}{5}}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

Rewrite the square root of the division \sqrt{\frac{8}{5}} as the division of square roots \frac{\sqrt{8}}{\sqrt{5}}.

$$\frac{\frac{\sqrt{8}}{\sqrt{5}}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{\frac{2\sqrt{2}}{\sqrt{5}}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

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

$$\frac{\frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

The square of \sqrt{5} is 5.

$$\frac{\frac{2\sqrt{2}\sqrt{5}}{5}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

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

$$\frac{\frac{2\sqrt{10}}{5}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

Express \frac{\frac{2\sqrt{10}}{5}}{22} as a single fraction.

$$\frac{2\sqrt{10}}{5\times 22}\sqrt{\frac{1}{5}}\sqrt{63}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{10}}{5\times 11}\sqrt{\frac{1}{5}}\sqrt{63}$$

Multiply 5 and 11 to get 55.

$$\frac{\sqrt{10}}{55}\sqrt{\frac{1}{5}}\sqrt{63}$$

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

$$\frac{\sqrt{10}}{55}\times \frac{\sqrt{1}}{\sqrt{5}}\sqrt{63}$$

Calculate the square root of 1 and get 1.

$$\frac{\sqrt{10}}{55}\times \frac{1}{\sqrt{5}}\sqrt{63}$$

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

$$\frac{\sqrt{10}}{55}\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{63}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{10}}{55}\times \frac{\sqrt{5}}{5}\sqrt{63}$$

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$\frac{\sqrt{10}}{55}\times \frac{\sqrt{5}}{5}\times 3\sqrt{7}$$

Multiply \frac{\sqrt{10}}{55} times \frac{\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{10}\sqrt{5}}{55\times 5}\times 3\sqrt{7}$$

Express \frac{\sqrt{10}\sqrt{5}}{55\times 5}\times 3 as a single fraction.

$$\frac{\sqrt{10}\sqrt{5}\times 3}{55\times 5}\sqrt{7}$$

Express \frac{\sqrt{10}\sqrt{5}\times 3}{55\times 5}\sqrt{7} as a single fraction.

$$\frac{\sqrt{10}\sqrt{5}\times 3\sqrt{7}}{55\times 5}$$

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}.

$$\frac{\sqrt{5}\sqrt{2}\sqrt{5}\times 3\sqrt{7}}{55\times 5}$$

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

$$\frac{5\sqrt{2}\times 3\sqrt{7}}{55\times 5}$$

Multiply 5 and 3 to get 15.

$$\frac{15\sqrt{2}\sqrt{7}}{55\times 5}$$

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{15\sqrt{14}}{55\times 5}$$

Multiply 55 and 5 to get 275.

$$\frac{15\sqrt{14}}{275}$$

Divide 15\sqrt{14} by 275 to get \frac{3}{55}\sqrt{14}.

$$\frac{3}{55}\sqrt{14}$$