Solve 5/3sqrt{3/2*3/10}sqrt{4/9}

$$\frac { 5 } { 3 } \sqrt { \frac { 3 } { 2 } \times \frac { 3 } { 10 } } \sqrt { \frac { 4 } { 9 } }$$

Evaluate

$$\frac{\sqrt{5}}{3}\approx 0.745355992$$

Solution Steps

Multiply \frac{3}{2} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{3}\sqrt{\frac{3\times 3}{2\times 10}}\sqrt{\frac{4}{9}}$$

Do the multiplications in the fraction \frac{3\times 3}{2\times 10}.

$$\frac{5}{3}\sqrt{\frac{9}{20}}\sqrt{\frac{4}{9}}$$

Rewrite the square root of the division \sqrt{\frac{9}{20}} as the division of square roots \frac{\sqrt{9}}{\sqrt{20}}.

$$\frac{5}{3}\times \frac{\sqrt{9}}{\sqrt{20}}\sqrt{\frac{4}{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{5}{3}\times \frac{3}{\sqrt{20}}\sqrt{\frac{4}{9}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{5}{3}\times \frac{3}{2\sqrt{5}}\sqrt{\frac{4}{9}}$$

Rationalize the denominator of \frac{3}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{5}{3}\times \frac{3\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}\sqrt{\frac{4}{9}}$$

The square of \sqrt{5} is 5.

$$\frac{5}{3}\times \frac{3\sqrt{5}}{2\times 5}\sqrt{\frac{4}{9}}$$

Multiply 2 and 5 to get 10.

$$\frac{5}{3}\times \frac{3\sqrt{5}}{10}\sqrt{\frac{4}{9}}$$

Rewrite the square root of the division \frac{4}{9} as the division of square roots \frac{\sqrt{4}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{5}{3}\times \frac{3\sqrt{5}}{10}\times \frac{2}{3}$$

Multiply \frac{5}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 2}{3\times 3}\times \frac{3\sqrt{5}}{10}$$

Do the multiplications in the fraction \frac{5\times 2}{3\times 3}.

$$\frac{10}{9}\times \frac{3\sqrt{5}}{10}$$

Multiply \frac{10}{9} times \frac{3\sqrt{5}}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 3\sqrt{5}}{9\times 10}$$

Cancel out 3\times 10 in both numerator and denominator.

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