Solve sqrt{2^2+{left(5/2right)}^2+7/2}

$$\sqrt{ { 2 }^{ 2 } + { \left( \frac{ 5 }{ 2 } \right) }^{ 2 } + \frac{ 7 }{ 2 } }$$

Evaluate

$$\frac{\sqrt{55}}{2}\approx 3.708099244$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4+\left(\frac{5}{2}\right)^{2}+\frac{7}{2}}$$

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

$$\sqrt{4+\frac{25}{4}+\frac{7}{2}}$$

Convert 4 to fraction \frac{16}{4}.

$$\sqrt{\frac{16}{4}+\frac{25}{4}+\frac{7}{2}}$$

Since \frac{16}{4} and \frac{25}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{16+25}{4}+\frac{7}{2}}$$

Add 16 and 25 to get 41.

$$\sqrt{\frac{41}{4}+\frac{7}{2}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{41}{4} and \frac{7}{2} to fractions with denominator 4.

$$\sqrt{\frac{41}{4}+\frac{14}{4}}$$

Since \frac{41}{4} and \frac{14}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{41+14}{4}}$$

Add 41 and 14 to get 55.

$$\sqrt{\frac{55}{4}}$$

Rewrite the square root of the division \sqrt{\frac{55}{4}} as the division of square roots \frac{\sqrt{55}}{\sqrt{4}}.

$$\frac{\sqrt{55}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{55}}{2}$$