Solve sqrt{1/16+1/25}

$$\sqrt{ \frac{ 1 }{ 16 } + \frac{ 1 }{ 25 } }$$

Evaluate

$$\frac{\sqrt{41}}{20}\approx 0.320156212$$

Solution Steps

Least common multiple of 16 and 25 is 400. Convert \frac{1}{16} and \frac{1}{25} to fractions with denominator 400.

$$\sqrt{\frac{25}{400}+\frac{16}{400}}$$

Since \frac{25}{400} and \frac{16}{400} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{25+16}{400}}$$

Add 25 and 16 to get 41.

$$\sqrt{\frac{41}{400}}$$

Rewrite the square root of the division \sqrt{\frac{41}{400}} as the division of square roots \frac{\sqrt{41}}{\sqrt{400}}.

$$\frac{\sqrt{41}}{\sqrt{400}}$$

Calculate the square root of 400 and get 20.

$$\frac{\sqrt{41}}{20}$$