Solve sqrt{(11/4)^2+1+16}

$$\sqrt { ( \frac { 11 } { 4 } ) ^ { 2 } + 1 + 16 }$$

Evaluate

$$\frac{\sqrt{393}}{4}\approx 4.9560569$$

Solution Steps

Calculate \frac{11}{4} to the power of 2 and get \frac{121}{16}.

$$\sqrt{\frac{121}{16}+1+16}$$

Convert 1 to fraction \frac{16}{16}.

$$\sqrt{\frac{121}{16}+\frac{16}{16}+16}$$

Since \frac{121}{16} and \frac{16}{16} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{121+16}{16}+16}$$

Add 121 and 16 to get 137.

$$\sqrt{\frac{137}{16}+16}$$

Convert 16 to fraction \frac{256}{16}.

$$\sqrt{\frac{137}{16}+\frac{256}{16}}$$

Since \frac{137}{16} and \frac{256}{16} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{137+256}{16}}$$

Add 137 and 256 to get 393.

$$\sqrt{\frac{393}{16}}$$

Rewrite the square root of the division \sqrt{\frac{393}{16}} as the division of square roots \frac{\sqrt{393}}{\sqrt{16}}.

$$\frac{\sqrt{393}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{\sqrt{393}}{4}$$