Solve sqrt{16/121}+sqrt{25/81}

$$\sqrt{ \frac{ 16 }{ 121 } } + \sqrt{ \frac{ 25 }{ 81 } }$$

Evaluate

$$\frac{91}{99}\approx 0.919191919$$

Solution Steps

Rewrite the square root of the division \frac{16}{121} as the division of square roots \frac{\sqrt{16}}{\sqrt{121}}. Take the square root of both numerator and denominator.

$$\frac{4}{11}+\sqrt{\frac{25}{81}}$$

Rewrite the square root of the division \frac{25}{81} as the division of square roots \frac{\sqrt{25}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$\frac{4}{11}+\frac{5}{9}$$

Least common multiple of 11 and 9 is 99. Convert \frac{4}{11} and \frac{5}{9} to fractions with denominator 99.

$$\frac{36}{99}+\frac{55}{99}$$

Since \frac{36}{99} and \frac{55}{99} have the same denominator, add them by adding their numerators.

$$\frac{36+55}{99}$$

Add 36 and 55 to get 91.

$$\frac{91}{99}$$

Factor

$$\frac{7 \cdot 13}{3 ^ {2} \cdot 11} = 0.9191919191919192$$