Solve sqrt{frac{121/4}+4}{sqrt{4}}

$$\frac{ \sqrt{ \frac{ 121 }{ 4 } } +4 }{ \sqrt{ 4 } }$$

Evaluate

$$\frac{19}{4}=4.75$$

Solution Steps

Rewrite the square root of the division \frac{121}{4} as the division of square roots \frac{\sqrt{121}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{\frac{11}{2}+4}{\sqrt{4}}$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{\frac{11}{2}+\frac{8}{2}}{\sqrt{4}}$$

Since \frac{11}{2} and \frac{8}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11+8}{2}}{\sqrt{4}}$$

Add 11 and 8 to get 19.

$$\frac{\frac{19}{2}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\frac{19}{2}}{2}$$

Express \frac{\frac{19}{2}}{2} as a single fraction.

$$\frac{19}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{19}{4}$$

Factor

$$\frac{19}{2 ^ {2}} = 4\frac{3}{4} = 4.75$$