Solve sqrt{1/2+3/4}

$$\sqrt{ \frac{ 1 }{ 2 } + \frac{ 3 }{ 4 } }$$

Evaluate

$$\frac{\sqrt{5}}{2}\approx 1.118033989$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\sqrt{\frac{2}{4}+\frac{3}{4}}$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{2+3}{4}}$$

Add 2 and 3 to get 5.

$$\sqrt{\frac{5}{4}}$$

Rewrite the square root of the division \sqrt{\frac{5}{4}} as the division of square roots \frac{\sqrt{5}}{\sqrt{4}}.

$$\frac{\sqrt{5}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{5}}{2}$$