Solve sqrt{(5/2)^2+5^2}

$$\sqrt { ( \frac { 5 } { 2 } ) ^ { 2 } + 5 ^ { 2 } }$$

Evaluate

$$\frac{5\sqrt{5}}{2}\approx 5.590169944$$

Solution Steps

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

$$\sqrt{\frac{25}{4}+5^{2}}$$

Calculate 5 to the power of 2 and get 25.

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

Convert 25 to fraction \frac{100}{4}.

$$\sqrt{\frac{25}{4}+\frac{100}{4}}$$

Since \frac{25}{4} and \frac{100}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{25+100}{4}}$$

Add 25 and 100 to get 125.

$$\sqrt{\frac{125}{4}}$$

Rewrite the square root of the division \sqrt{\frac{125}{4}} as the division of square roots \frac{\sqrt{125}}{\sqrt{4}}.

$$\frac{\sqrt{125}}{\sqrt{4}}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$\frac{5\sqrt{5}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{5\sqrt{5}}{2}$$