Solve sqrt{(366)^2+(482/9)}

$$\sqrt { ( 366 ) ^ { 2 } + ( 48 \frac { 2 } { 9 } ) }$$

Evaluate

$$\frac{\sqrt{1206038}}{3}\approx 366.065871425$$

Solution Steps

Calculate 366 to the power of 2 and get 133956.

$$\sqrt{133956+\frac{48\times 9+2}{9}}$$

Multiply 48 and 9 to get 432.

$$\sqrt{133956+\frac{432+2}{9}}$$

Add 432 and 2 to get 434.

$$\sqrt{133956+\frac{434}{9}}$$

Convert 133956 to fraction \frac{1205604}{9}.

$$\sqrt{\frac{1205604}{9}+\frac{434}{9}}$$

Since \frac{1205604}{9} and \frac{434}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{1205604+434}{9}}$$

Add 1205604 and 434 to get 1206038.

$$\sqrt{\frac{1206038}{9}}$$

Rewrite the square root of the division \sqrt{\frac{1206038}{9}} as the division of square roots \frac{\sqrt{1206038}}{\sqrt{9}}.

$$\frac{\sqrt{1206038}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{\sqrt{1206038}}{3}$$