Solve sqrt{1/4+1/49}

$$\sqrt{ \frac{ 1 }{ 4 } + \frac{ 1 }{ 49 } }$$

Evaluate

$$\frac{\sqrt{53}}{14}\approx 0.520007849$$

Solution Steps

Least common multiple of 4 and 49 is 196. Convert \frac{1}{4} and \frac{1}{49} to fractions with denominator 196.

$$\sqrt{\frac{49}{196}+\frac{4}{196}}$$

Since \frac{49}{196} and \frac{4}{196} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{49+4}{196}}$$

Add 49 and 4 to get 53.

$$\sqrt{\frac{53}{196}}$$

Rewrite the square root of the division \sqrt{\frac{53}{196}} as the division of square roots \frac{\sqrt{53}}{\sqrt{196}}.

$$\frac{\sqrt{53}}{\sqrt{196}}$$

Calculate the square root of 196 and get 14.

$$\frac{\sqrt{53}}{14}$$