Solve sqrt{144+25*3/4}

$$\sqrt{ 144+ \frac{ 25 \times 3 }{ 4 } }$$

Evaluate

$$\frac{\sqrt{651}}{2}\approx 12.757350822$$

Solution Steps

Multiply 25 and 3 to get 75.

$$\sqrt{144+\frac{75}{4}}$$

Convert 144 to fraction \frac{576}{4}.

$$\sqrt{\frac{576}{4}+\frac{75}{4}}$$

Since \frac{576}{4} and \frac{75}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{576+75}{4}}$$

Add 576 and 75 to get 651.

$$\sqrt{\frac{651}{4}}$$

Rewrite the square root of the division \sqrt{\frac{651}{4}} as the division of square roots \frac{\sqrt{651}}{\sqrt{4}}.

$$\frac{\sqrt{651}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{651}}{2}$$