Solve sqrt{11/4}*sqrt{22/5}*sqrt{3}

$$\sqrt { 1 \frac { 1 } { 4 } } \times \sqrt { 2 \frac { 2 } { 5 } } \times \sqrt { 3 }$$

Evaluate

$$3$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\sqrt{\frac{4+1}{4}}\sqrt{\frac{2\times 5+2}{5}}\sqrt{3}$$

Add 4 and 1 to get 5.

$$\sqrt{\frac{5}{4}}\sqrt{\frac{2\times 5+2}{5}}\sqrt{3}$$

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

$$\frac{\sqrt{5}}{\sqrt{4}}\sqrt{\frac{2\times 5+2}{5}}\sqrt{3}$$

Calculate the square root of 4 and get 2.

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

Multiply 2 and 5 to get 10.

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

Add 10 and 2 to get 12.

$$\frac{\sqrt{5}}{2}\sqrt{\frac{12}{5}}\sqrt{3}$$

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

$$\frac{\sqrt{5}}{2}\times \frac{\sqrt{12}}{\sqrt{5}}\sqrt{3}$$

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}.

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

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

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

The square of \sqrt{5} is 5.

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

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

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

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

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

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{5}\sqrt{15}}{5}\sqrt{3}$$

Express \frac{\sqrt{5}\sqrt{15}}{5}\sqrt{3} as a single fraction.

$$\frac{\sqrt{5}\sqrt{15}\sqrt{3}}{5}$$

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

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

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

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

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

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

Multiply 5 and 3 to get 15.

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

Divide 15 by 5 to get 3.

$$3$$

Factor

$$3$$