Solve sqrt{(44/25)^2+(117/25)}

$$\sqrt { ( \frac { 44 } { 25 } ) ^ { 2 } + ( \frac { 117 } { 25 } ) }$$

Evaluate

$$\frac{\sqrt{4861}}{25}\approx 2.788834882$$

Solution Steps

Calculate \frac{44}{25} to the power of 2 and get \frac{1936}{625}.

$$\sqrt{\frac{1936}{625}+\frac{117}{25}}$$

Least common multiple of 625 and 25 is 625. Convert \frac{1936}{625} and \frac{117}{25} to fractions with denominator 625.

$$\sqrt{\frac{1936}{625}+\frac{2925}{625}}$$

Since \frac{1936}{625} and \frac{2925}{625} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{1936+2925}{625}}$$

Add 1936 and 2925 to get 4861.

$$\sqrt{\frac{4861}{625}}$$

Rewrite the square root of the division \sqrt{\frac{4861}{625}} as the division of square roots \frac{\sqrt{4861}}{\sqrt{625}}.

$$\frac{\sqrt{4861}}{\sqrt{625}}$$

Calculate the square root of 625 and get 25.

$$\frac{\sqrt{4861}}{25}$$