Solve sqrt{50/49+1/64}=

$$\sqrt { \frac { 50 } { 49 } + \frac { 1 } { 64 } } =$$

Evaluate

$$\frac{57}{56}\approx 1.017857143$$

Solution Steps

Least common multiple of 49 and 64 is 3136. Convert \frac{50}{49} and \frac{1}{64} to fractions with denominator 3136.

$$\sqrt{\frac{3200}{3136}+\frac{49}{3136}}$$

Since \frac{3200}{3136} and \frac{49}{3136} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{3200+49}{3136}}$$

Add 3200 and 49 to get 3249.

$$\sqrt{\frac{3249}{3136}}$$

Rewrite the square root of the division \frac{3249}{3136} as the division of square roots \frac{\sqrt{3249}}{\sqrt{3136}}. Take the square root of both numerator and denominator.

$$\frac{57}{56}$$

Factor

$$\frac{3 \cdot 19}{2 ^ {3} \cdot 7} = 1\frac{1}{56} = 1.0178571428571428$$