Solve sqrt{240^2+360^2+1,2^2}

$$\sqrt { 240 ^ { 2 } + 360 ^ { 2 } + 1,2 ^ { 2 } }$$

Evaluate

$$2\sqrt{46801}\approx 432.670775533$$

Solution Steps

Calculate 240 to the power of 2 and get 57600.

$$\sqrt{57600+360^{2}+1\times 2^{2}}$$

Calculate 360 to the power of 2 and get 129600.

$$\sqrt{57600+129600+1\times 2^{2}}$$

Add 57600 and 129600 to get 187200.

$$\sqrt{187200+1\times 2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{187200+1\times 4}$$

Multiply 1 and 4 to get 4.

$$\sqrt{187200+4}$$

Add 187200 and 4 to get 187204.

$$\sqrt{187204}$$

Factor 187204=2^{2}\times 46801. Rewrite the square root of the product \sqrt{2^{2}\times 46801} as the product of square roots \sqrt{2^{2}}\sqrt{46801}. Take the square root of 2^{2}.

$$2\sqrt{46801}$$