Solve sqrt{5/12}*sqrt{8/25}*sqrt{3/12}

$$\sqrt { \frac { 5 } { 12 } } \cdot \sqrt { \frac { 8 } { 25 } } \cdot \sqrt { \frac { 3 } { 12 } }$$

Evaluate

$$\frac{\sqrt{30}}{30}\approx 0.182574186$$

Solution Steps

To multiply \sqrt{\frac{5}{12}} and \sqrt{\frac{8}{25}}, multiply the numbers under the square root.

$$\sqrt{\frac{2}{15}}\sqrt{\frac{3}{12}}$$

Rewrite the square root of the division \sqrt{\frac{2}{15}} as the division of square roots \frac{\sqrt{2}}{\sqrt{15}}.

$$\frac{\sqrt{2}}{\sqrt{15}}\sqrt{\frac{3}{12}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\sqrt{2}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}\sqrt{\frac{3}{12}}$$

The square of \sqrt{15} is 15.

$$\frac{\sqrt{2}\sqrt{15}}{15}\sqrt{\frac{3}{12}}$$

To multiply \sqrt{2} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{15}\sqrt{\frac{3}{12}}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\sqrt{30}}{15}\sqrt{\frac{1}{4}}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{\sqrt{30}}{15}\times \frac{1}{2}$$

Multiply \frac{\sqrt{30}}{15} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{30}}{15\times 2}$$

Multiply 15 and 2 to get 30.

$$\frac{\sqrt{30}}{30}$$