Solve sqrt{3/2}*5/6*sqrt{8/15*3/2}=

$$\sqrt { \frac { 3 } { 2 } } \cdot \frac { 5 } { 6 } \cdot \sqrt { \frac { 8 } { 15 } \cdot \frac { 3 } { 2 } } =$$

Evaluate

$$\frac{\sqrt{30}}{6}\approx 0.912870929$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

$$\frac{\sqrt{3}}{\sqrt{2}}\times \frac{5}{6}\sqrt{\frac{8}{15}\times \frac{3}{2}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{5}{6}\sqrt{\frac{8}{15}\times \frac{3}{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3}\sqrt{2}}{2}\times \frac{5}{6}\sqrt{\frac{8}{15}\times \frac{3}{2}}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{2}\times \frac{5}{6}\sqrt{\frac{8}{15}\times \frac{3}{2}}$$

Multiply \frac{8}{15} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{6}}{2}\times \frac{5}{6}\sqrt{\frac{8\times 3}{15\times 2}}$$

Do the multiplications in the fraction \frac{8\times 3}{15\times 2}.

$$\frac{\sqrt{6}}{2}\times \frac{5}{6}\sqrt{\frac{24}{30}}$$

Reduce the fraction \frac{24}{30} to lowest terms by extracting and canceling out 6.

$$\frac{\sqrt{6}}{2}\times \frac{5}{6}\sqrt{\frac{4}{5}}$$

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

$$\frac{\sqrt{6}}{2}\times \frac{5}{6}\times \frac{\sqrt{4}}{\sqrt{5}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{6}}{2}\times \frac{5}{6}\times \frac{2}{\sqrt{5}}$$

Rationalize the denominator of \frac{2}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{6}}{2}\times \frac{5}{6}\times \frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{6}}{2}\times \frac{5}{6}\times \frac{2\sqrt{5}}{5}$$

Multiply \frac{\sqrt{6}}{2} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{6}\times 5}{2\times 6}\times \frac{2\sqrt{5}}{5}$$

Multiply \frac{\sqrt{6}\times 5}{2\times 6} times \frac{2\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{6}\times 5\times 2\sqrt{5}}{2\times 6\times 5}$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{\sqrt{5}\sqrt{6}}{6}$$

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{6}$$