Solve 1/3sqrt{0.75}*3/5sqrt{5/12}

$$\frac{ 1 }{ 3 } \sqrt{ 0.75 } \times \frac{ 3 }{ 5 } \sqrt{ \frac{ 5 }{ 12 } }$$

Evaluate

$$\frac{\sqrt{5}}{20}\approx 0.111803399$$

Solution Steps

To multiply \sqrt{0.75} and \sqrt{\frac{5}{12}}, multiply the numbers under the square root.

$$\frac{1}{3}\sqrt{\frac{5}{16}}\times \frac{3}{5}$$

Rewrite the square root of the division \sqrt{\frac{5}{16}} as the division of square roots \frac{\sqrt{5}}{\sqrt{16}}.

$$\frac{1}{3}\times \frac{\sqrt{5}}{\sqrt{16}}\times \frac{3}{5}$$

Calculate the square root of 16 and get 4.

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

Multiply \frac{1}{3} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Multiply \frac{1}{5} times \frac{\sqrt{5}}{4} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 5 and 4 to get 20.

$$\frac{\sqrt{5}}{20}$$