Solve 3/3sqrt{9/5}div1/5sqrt{1/5}=

$$\frac { 3 } { 3 } \sqrt { \frac { 9 } { 5 } } \div \frac { 1 } { 5 } \sqrt { \frac { 1 } { 5 } } =$$

Evaluate

$$3$$

Solution Steps

Divide 3 by 3 to get 1.

$$\frac{1\sqrt{\frac{9}{5}}}{\frac{1}{5}}\sqrt{\frac{1}{5}}$$

Rewrite the square root of the division \sqrt{\frac{9}{5}} as the division of square roots \frac{\sqrt{9}}{\sqrt{5}}.

$$\frac{1\times \frac{\sqrt{9}}{\sqrt{5}}}{\frac{1}{5}}\sqrt{\frac{1}{5}}$$

Calculate the square root of 9 and get 3.

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

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

$$\frac{1\times \frac{3\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}{\frac{1}{5}}\sqrt{\frac{1}{5}}$$

The square of \sqrt{5} is 5.

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

Express 1\times \frac{3\sqrt{5}}{5} as a single fraction.

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

Divide \frac{3\sqrt{5}}{5} by \frac{1}{5} by multiplying \frac{3\sqrt{5}}{5} by the reciprocal of \frac{1}{5}.

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

Cancel out 5 and 5.

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

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

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

Calculate the square root of 1 and get 1.

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

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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

Express 3\times \frac{\sqrt{5}}{5} as a single fraction.

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

Express \frac{3\sqrt{5}}{5}\sqrt{5} as a single fraction.

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

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

$$\frac{3\times 5}{5}$$

Cancel out 5 and 5.

$$3$$

Factor

$$3$$