Solve sqrt{12/3}*sqrt{15/4}

$$\sqrt { 1 \frac { 2 } { 3 } } \times \sqrt { \frac { 15 } { 4 } }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\sqrt{\frac{3+2}{3}}\sqrt{\frac{15}{4}}$$

Add 3 and 2 to get 5.

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

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

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

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

$$\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{\frac{15}{4}}$$

The square of \sqrt{3} is 3.

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

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

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

Rewrite the square root of the division \sqrt{\frac{15}{4}} as the division of square roots \frac{\sqrt{15}}{\sqrt{4}}.

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

Calculate the square root of 4 and get 2.

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

Multiply \frac{\sqrt{15}}{3} times \frac{\sqrt{15}}{2} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply 3 and 2 to get 6.

$$\frac{15}{6}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$