Solve sqrt{36+1/4}

$$\sqrt { 36 + \frac { 1 } { 4 } }$$

Evaluate

$$\frac{\sqrt{145}}{2}\approx 6.020797289$$

Solution Steps

Convert 36 to fraction \frac{144}{4}.

$$\sqrt{\frac{144}{4}+\frac{1}{4}}$$

Since \frac{144}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{144+1}{4}}$$

Add 144 and 1 to get 145.

$$\sqrt{\frac{145}{4}}$$

Rewrite the square root of the division \sqrt{\frac{145}{4}} as the division of square roots \frac{\sqrt{145}}{\sqrt{4}}.

$$\frac{\sqrt{145}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{145}}{2}$$