Solve 2(3/2sqrt{12/3}*sqrt{11/4})

$$2( \frac{ 3 }{ 2 } \sqrt{ 1 \frac{ 2 }{ 3 } } \times \sqrt{ 1 \frac{ 1 }{ 4 } } )$$

Evaluate

$$\frac{5\sqrt{3}}{2}\approx 4.330127019$$

Solution Steps

Cancel out 2 and 2.

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

Multiply 1 and 3 to get 3.

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

Add 3 and 2 to get 5.

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

Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.

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

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

$$3\times \frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{\frac{1\times 4+1}{4}}$$

The square of \sqrt{3} is 3.

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

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

$$3\times \frac{\sqrt{15}}{3}\sqrt{\frac{1\times 4+1}{4}}$$

Multiply 1 and 4 to get 4.

$$3\times \frac{\sqrt{15}}{3}\sqrt{\frac{4+1}{4}}$$

Add 4 and 1 to get 5.

$$3\times \frac{\sqrt{15}}{3}\sqrt{\frac{5}{4}}$$

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

$$3\times \frac{\sqrt{15}}{3}\times \frac{\sqrt{5}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

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

Cancel out 3 and 3.

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

Express \sqrt{15}\times \frac{\sqrt{5}}{2} as a single fraction.

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

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}.

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

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

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