Solve sqrt{2^2+(21/4)^2}

$$\sqrt { 2 ^ { 2 } + ( \frac { 21 } { 4 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{505}}{4}\approx 5.618051264$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4+\left(\frac{21}{4}\right)^{2}}$$

Calculate \frac{21}{4} to the power of 2 and get \frac{441}{16}.

$$\sqrt{4+\frac{441}{16}}$$

Convert 4 to fraction \frac{64}{16}.

$$\sqrt{\frac{64}{16}+\frac{441}{16}}$$

Since \frac{64}{16} and \frac{441}{16} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{64+441}{16}}$$

Add 64 and 441 to get 505.

$$\sqrt{\frac{505}{16}}$$

Rewrite the square root of the division \sqrt{\frac{505}{16}} as the division of square roots \frac{\sqrt{505}}{\sqrt{16}}.

$$\frac{\sqrt{505}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{\sqrt{505}}{4}$$