Solve 2/3sqrt{7/15}*3/4sqrt{10/21}

$$\frac { 2 } { 3 } \sqrt { \frac { 7 } { 15 } } \times \frac { 3 } { 4 } \sqrt { \frac { 10 } { 21 } }$$

Evaluate

$$\frac{\sqrt{2}}{6}\approx 0.23570226$$

Solution Steps

To multiply \sqrt{\frac{7}{15}} and \sqrt{\frac{10}{21}}, multiply the numbers under the square root.

$$\frac{2}{3}\sqrt{\frac{2}{9}}\times \frac{3}{4}$$

Rewrite the square root of the division \sqrt{\frac{2}{9}} as the division of square roots \frac{\sqrt{2}}{\sqrt{9}}.

$$\frac{2}{3}\times \frac{\sqrt{2}}{\sqrt{9}}\times \frac{3}{4}$$

Calculate the square root of 9 and get 3.

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

Multiply \frac{2}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Multiply \frac{1}{2} times \frac{\sqrt{2}}{3} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{\sqrt{2}}{6}$$