Solve sqrt{11/5}2sqrt{3}-1/2sqrt{10}

$$\sqrt{ 1 \frac{ 1 }{ 5 } } 2 \sqrt{ 3 } - \frac{ 1 }{ 2 } \sqrt{ 10 }$$

Evaluate

$$\frac{7\sqrt{10}}{10}\approx 2.213594362$$

Solution Steps

Multiply 1 and 5 to get 5.

$$2\sqrt{\frac{5+1}{5}}\sqrt{3}-\frac{1}{2}\sqrt{10}$$

Add 5 and 1 to get 6.

$$2\sqrt{\frac{6}{5}}\sqrt{3}-\frac{1}{2}\sqrt{10}$$

Rewrite the square root of the division \sqrt{\frac{6}{5}} as the division of square roots \frac{\sqrt{6}}{\sqrt{5}}.

$$2\times \frac{\sqrt{6}}{\sqrt{5}}\sqrt{3}-\frac{1}{2}\sqrt{10}$$

Rationalize the denominator of \frac{\sqrt{6}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$2\times \frac{\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{3}-\frac{1}{2}\sqrt{10}$$

The square of \sqrt{5} is 5.

$$2\times \frac{\sqrt{6}\sqrt{5}}{5}\sqrt{3}-\frac{1}{2}\sqrt{10}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$2\times \frac{\sqrt{30}}{5}\sqrt{3}-\frac{1}{2}\sqrt{10}$$

Express 2\times \frac{\sqrt{30}}{5} as a single fraction.

$$\frac{2\sqrt{30}}{5}\sqrt{3}-\frac{1}{2}\sqrt{10}$$

Express \frac{2\sqrt{30}}{5}\sqrt{3} as a single fraction.

$$\frac{2\sqrt{30}\sqrt{3}}{5}-\frac{1}{2}\sqrt{10}$$

Factor 30=3\times 10. Rewrite the square root of the product \sqrt{3\times 10} as the product of square roots \sqrt{3}\sqrt{10}.

$$\frac{2\sqrt{3}\sqrt{10}\sqrt{3}}{5}-\frac{1}{2}\sqrt{10}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{2\times 3\sqrt{10}}{5}-\frac{1}{2}\sqrt{10}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{10}}{5}-\frac{1}{2}\sqrt{10}$$

Combine \frac{6\sqrt{10}}{5} and -\frac{1}{2}\sqrt{10} to get \frac{7}{10}\sqrt{10}.

$$\frac{7}{10}\sqrt{10}$$