Solve -sqrt{131/4}+9/2

$$- \sqrt{ 13 \frac{ 1 }{ 4 } } + \frac{ 9 }{ 2 }$$

Evaluate

$$\frac{9-\sqrt{53}}{2}\approx 0.859945055$$

Solution Steps

Multiply 13 and 4 to get 52.

$$-\sqrt{\frac{52+1}{4}}+\frac{9}{2}$$

Add 52 and 1 to get 53.

$$-\sqrt{\frac{53}{4}}+\frac{9}{2}$$

Rewrite the square root of the division \sqrt{\frac{53}{4}} as the division of square roots \frac{\sqrt{53}}{\sqrt{4}}.

$$-\frac{\sqrt{53}}{\sqrt{4}}+\frac{9}{2}$$

Calculate the square root of 4 and get 2.

$$-\frac{\sqrt{53}}{2}+\frac{9}{2}$$

Since \frac{\sqrt{53}}{2} and \frac{9}{2} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{53}+9}{2}$$

Factor

$$\frac{9 - \sqrt{53}}{2} = 0.859945055359741$$