Solve sqrt{196/25+64/25}

$$\sqrt { \frac { 196 } { 25 } + \frac { 64 } { 25 } }$$

Evaluate

$$\frac{2\sqrt{65}}{5}\approx 3.224903099$$

Solution Steps

Since \frac{196}{25} and \frac{64}{25} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{196+64}{25}}$$

Add 196 and 64 to get 260.

$$\sqrt{\frac{260}{25}}$$

Reduce the fraction \frac{260}{25} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{52}{5}}$$

Rewrite the square root of the division \sqrt{\frac{52}{5}} as the division of square roots \frac{\sqrt{52}}{\sqrt{5}}.

$$\frac{\sqrt{52}}{\sqrt{5}}$$

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$\frac{2\sqrt{13}}{\sqrt{5}}$$

Rationalize the denominator of \frac{2\sqrt{13}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{13}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{13}\sqrt{5}}{5}$$

To multiply \sqrt{13} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{2\sqrt{65}}{5}$$