Solve (2)-sqrt{19}divsqrt{95}*sqrt{1/5}

$$( 2 ) - \sqrt { 19 } \div \sqrt { 95 } \times \sqrt { \frac { 1 } { 5 } }$$

Evaluate

$$\frac{9}{5}=1.8$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{19}}{\sqrt{95}} by multiplying numerator and denominator by \sqrt{95}.

$$2-\frac{\sqrt{19}\sqrt{95}}{\left(\sqrt{95}\right)^{2}}\sqrt{\frac{1}{5}}$$

The square of \sqrt{95} is 95.

$$2-\frac{\sqrt{19}\sqrt{95}}{95}\sqrt{\frac{1}{5}}$$

Factor 95=19\times 5. Rewrite the square root of the product \sqrt{19\times 5} as the product of square roots \sqrt{19}\sqrt{5}.

$$2-\frac{\sqrt{19}\sqrt{19}\sqrt{5}}{95}\sqrt{\frac{1}{5}}$$

Multiply \sqrt{19} and \sqrt{19} to get 19.

$$2-\frac{19\sqrt{5}}{95}\sqrt{\frac{1}{5}}$$

Divide 19\sqrt{5} by 95 to get \frac{1}{5}\sqrt{5}.

$$2-\frac{1}{5}\sqrt{5}\sqrt{\frac{1}{5}}$$

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

$$2-\frac{1}{5}\sqrt{5}\times \frac{\sqrt{1}}{\sqrt{5}}$$

Calculate the square root of 1 and get 1.

$$2-\frac{1}{5}\sqrt{5}\times \frac{1}{\sqrt{5}}$$

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

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

The square of \sqrt{5} is 5.

$$2-\frac{1}{5}\sqrt{5}\times \frac{\sqrt{5}}{5}$$

Multiply \frac{1}{5} times \frac{\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 5 and 5 to get 25.

$$2-\frac{\sqrt{5}}{25}\sqrt{5}$$

Express \frac{\sqrt{5}}{25}\sqrt{5} as a single fraction.

$$2-\frac{\sqrt{5}\sqrt{5}}{25}$$

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

$$2-\frac{5}{25}$$

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

$$2-\frac{1}{5}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{10}{5}-\frac{1}{5}$$

Since \frac{10}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-1}{5}$$

Subtract 1 from 10 to get 9.

$$\frac{9}{5}$$

Factor

$$\frac{3 ^ {2}}{5} = 1\frac{4}{5} = 1.8$$