Solve 4/5+sqrt{15/25+396/5}

$$\frac { 4 } { 5 } + \sqrt { \frac { 15 } { 25 } + \frac { 396 } { 5 } }$$

Evaluate

$$\frac{\sqrt{1995}+4}{5}\approx 9.733084574$$

Solution Steps

Reduce the fraction \frac{15}{25} to lowest terms by extracting and canceling out 5.

$$\frac{4}{5}+\sqrt{\frac{3}{5}+\frac{396}{5}}$$

Since \frac{3}{5} and \frac{396}{5} have the same denominator, add them by adding their numerators.

$$\frac{4}{5}+\sqrt{\frac{3+396}{5}}$$

Add 3 and 396 to get 399.

$$\frac{4}{5}+\sqrt{\frac{399}{5}}$$

Rewrite the square root of the division \sqrt{\frac{399}{5}} as the division of square roots \frac{\sqrt{399}}{\sqrt{5}}.

$$\frac{4}{5}+\frac{\sqrt{399}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{399}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{4}{5}+\frac{\sqrt{399}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{4}{5}+\frac{\sqrt{399}\sqrt{5}}{5}$$

To multiply \sqrt{399} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{4}{5}+\frac{\sqrt{1995}}{5}$$

Since \frac{4}{5} and \frac{\sqrt{1995}}{5} have the same denominator, add them by adding their numerators.

$$\frac{4+\sqrt{1995}}{5}$$

Factor

$$\frac{\sqrt{1995} + 4}{5} = 9.733084573650917$$