Solve sqrt{(200sqrt{3})^2-1200^2}

$$\sqrt { ( 200 \sqrt { 3 } ) ^ { 2 } - 1200 ^ { 2 } }$$

Evaluate (complex solution)

$$200\sqrt{33}i\approx 1148.912529308i$$

Solution Steps

Expand \left(200\sqrt{3}\right)^{2}.

$$\sqrt{200^{2}\left(\sqrt{3}\right)^{2}-1200^{2}}$$

Calculate 200 to the power of 2 and get 40000.

$$\sqrt{40000\left(\sqrt{3}\right)^{2}-1200^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{40000\times 3-1200^{2}}$$

Multiply 40000 and 3 to get 120000.

$$\sqrt{120000-1200^{2}}$$

Calculate 1200 to the power of 2 and get 1440000.

$$\sqrt{120000-1440000}$$

Subtract 1440000 from 120000 to get -1320000.

$$\sqrt{-1320000}$$

Factor -1320000=\left(200i\right)^{2}\times 33. Rewrite the square root of the product \sqrt{\left(200i\right)^{2}\times 33} as the product of square roots \sqrt{\left(200i\right)^{2}}\sqrt{33}. Take the square root of \left(200i\right)^{2}.

$$200i\sqrt{33}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$