Solve sqrt{1+{left(22/4right)}^2}

$$\sqrt{ 1+ { \left( \frac{ 22 }{ 4 } \right) }^{ 2 } }$$

Evaluate

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

Solution Steps

Reduce the fraction \frac{22}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{1+\left(\frac{11}{2}\right)^{2}}$$

Calculate \frac{11}{2} to the power of 2 and get \frac{121}{4}.

$$\sqrt{1+\frac{121}{4}}$$

Add 1 and \frac{121}{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.

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