Solve sqrt{left(3+2right)^2+{left(-1/2+3right)}^2}

$$\sqrt{ { \left(3+2 \right) }^{ 2 } + { \left(- \frac{ 1 }{ 2 } +3 \right) }^{ 2 } }$$

Evaluate

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

Solution Steps

Add 3 and 2 to get 5.

$$\sqrt{5^{2}+\left(-\frac{1}{2}+3\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{25+\left(-\frac{1}{2}+3\right)^{2}}$$

Add -\frac{1}{2} and 3 to get \frac{5}{2}.

$$\sqrt{25+\left(\frac{5}{2}\right)^{2}}$$

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

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

Add 25 and \frac{25}{4} to get \frac{125}{4}.

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

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.

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