Solve sqrt{2*2000^2+2001^2}

$$\sqrt{ 2 \times { 2000 }^{ 2 } + { 2001 }^{ 2 } }$$

Evaluate

$$\sqrt{12004001}\approx 3464.679061616$$

Solution Steps

Calculate 2000 to the power of 2 and get 4000000.

$$\sqrt{2\times 4000000+2001^{2}}$$

Multiply 2 and 4000000 to get 8000000.

$$\sqrt{8000000+2001^{2}}$$

Calculate 2001 to the power of 2 and get 4004001.

$$\sqrt{8000000+4004001}$$

Add 8000000 and 4004001 to get 12004001.

$$\sqrt{12004001}$$