Solve sqrt{1440^2+1440^2+2*1440*1440*0.5}

$$\sqrt{ { 1440 }^{ 2 } + { 1440 }^{ 2 } +2 \times 1440 \times 1440 \times 0.5 }$$

Evaluate

$$1440\sqrt{3}\approx 2494.153162899$$

Solution Steps

Calculate 1440 to the power of 2 and get 2073600.

$$\sqrt{2073600+1440^{2}+2\times 1440\times 1440\times 0.5}$$

Calculate 1440 to the power of 2 and get 2073600.

$$\sqrt{2073600+2073600+2\times 1440\times 1440\times 0.5}$$

Add 2073600 and 2073600 to get 4147200.

$$\sqrt{4147200+2\times 1440\times 1440\times 0.5}$$

Multiply 2 and 1440 to get 2880.

$$\sqrt{4147200+2880\times 1440\times 0.5}$$

Multiply 2880 and 1440 to get 4147200.

$$\sqrt{4147200+4147200\times 0.5}$$

Multiply 4147200 and 0.5 to get 2073600.

$$\sqrt{4147200+2073600}$$

Add 4147200 and 2073600 to get 6220800.

$$\sqrt{6220800}$$

Factor 6220800=1440^{2}\times 3. Rewrite the square root of the product \sqrt{1440^{2}\times 3} as the product of square roots \sqrt{1440^{2}}\sqrt{3}. Take the square root of 1440^{2}.

$$1440\sqrt{3}$$