Solve sqrt{1+1/16}

$$\sqrt{ 1+ \frac{ 1 }{ 16 } }$$

Evaluate

$$\frac{\sqrt{17}}{4}\approx 1.030776406$$

Solution Steps

Convert 1 to fraction \frac{16}{16}.

$$\sqrt{\frac{16}{16}+\frac{1}{16}}$$

Since \frac{16}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{16+1}{16}}$$

Add 16 and 1 to get 17.

$$\sqrt{\frac{17}{16}}$$

Rewrite the square root of the division \sqrt{\frac{17}{16}} as the division of square roots \frac{\sqrt{17}}{\sqrt{16}}.

$$\frac{\sqrt{17}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{\sqrt{17}}{4}$$