Solve 3/4sqrt{1/10}div3/8sqrt{20/25}=

$$\frac { 3 } { 4 } \sqrt { \frac { 1 } { 10 } } \div \frac { 3 } { 8 } \sqrt { \frac { 20 } { 25 } } =$$

Evaluate

$$\frac{2\sqrt{2}}{5}\approx 0.565685425$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{10}} as the division of square roots \frac{\sqrt{1}}{\sqrt{10}}.

$$\frac{\frac{3}{4}\times \frac{\sqrt{1}}{\sqrt{10}}}{\frac{3}{8}}\sqrt{\frac{20}{25}}$$

Calculate the square root of 1 and get 1.

$$\frac{\frac{3}{4}\times \frac{1}{\sqrt{10}}}{\frac{3}{8}}\sqrt{\frac{20}{25}}$$

Rationalize the denominator of \frac{1}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\frac{3}{4}\times \frac{\sqrt{10}}{\left(\sqrt{10}\right)^{2}}}{\frac{3}{8}}\sqrt{\frac{20}{25}}$$

The square of \sqrt{10} is 10.

$$\frac{\frac{3}{4}\times \frac{\sqrt{10}}{10}}{\frac{3}{8}}\sqrt{\frac{20}{25}}$$

Multiply \frac{3}{4} times \frac{\sqrt{10}}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\sqrt{10}}{4\times 10}}{\frac{3}{8}}\sqrt{\frac{20}{25}}$$

Divide \frac{3\sqrt{10}}{4\times 10} by \frac{3}{8} by multiplying \frac{3\sqrt{10}}{4\times 10} by the reciprocal of \frac{3}{8}.

$$\frac{3\sqrt{10}\times 8}{4\times 10\times 3}\sqrt{\frac{20}{25}}$$

Cancel out 2\times 3\times 4 in both numerator and denominator.

$$\frac{\sqrt{10}}{5}\sqrt{\frac{20}{25}}$$

Reduce the fraction \frac{20}{25} to lowest terms by extracting and canceling out 5.

$$\frac{\sqrt{10}}{5}\sqrt{\frac{4}{5}}$$

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

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

Calculate the square root of 4 and get 2.

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

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

$$\frac{\sqrt{10}}{5}\times \frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

Multiply \frac{\sqrt{10}}{5} times \frac{2\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

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

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Multiply 5 and 2 to get 10.

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

Multiply 5 and 5 to get 25.

$$\frac{10\sqrt{2}}{25}$$

Divide 10\sqrt{2} by 25 to get \frac{2}{5}\sqrt{2}.

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