Solve sqrt{1+1/4}

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

Evaluate

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

Solution Steps

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{4}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

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

Add 4 and 1 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.

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