Solve sqrt{{left(-5/2right)}^2+8}

$$\sqrt{ { \left(- \frac{ 5 }{ 2 } \right) }^{ 2 } +8 }$$

Evaluate

$$\frac{\sqrt{57}}{2}\approx 3.774917218$$

Solution Steps

Calculate -\frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\sqrt{\frac{25}{4}+8}$$

Convert 8 to fraction \frac{32}{4}.

$$\sqrt{\frac{25}{4}+\frac{32}{4}}$$

Since \frac{25}{4} and \frac{32}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{25+32}{4}}$$

Add 25 and 32 to get 57.

$$\sqrt{\frac{57}{4}}$$

Rewrite the square root of the division \sqrt{\frac{57}{4}} as the division of square roots \frac{\sqrt{57}}{\sqrt{4}}.

$$\frac{\sqrt{57}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{57}}{2}$$