Solve sqrt{1/4}+9/4+22

$$\sqrt{ \frac{ 1 }{ 4 } } + \frac{ 9 }{ 4 } +22$$

Evaluate

$$\frac{99}{4}=24.75$$

Solution Steps

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{1}{2}+\frac{9}{4}+22$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{9}{4} to fractions with denominator 4.

$$\frac{2}{4}+\frac{9}{4}+22$$

Since \frac{2}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$\frac{2+9}{4}+22$$

Add 2 and 9 to get 11.

$$\frac{11}{4}+22$$

Convert 22 to fraction \frac{88}{4}.

$$\frac{11}{4}+\frac{88}{4}$$

Since \frac{11}{4} and \frac{88}{4} have the same denominator, add them by adding their numerators.

$$\frac{11+88}{4}$$

Add 11 and 88 to get 99.

$$\frac{99}{4}$$

Factor

$$\frac{3 ^ {2} \cdot 11}{2 ^ {2}} = 24\frac{3}{4} = 24.75$$