Solve sqrt{3000^2-4000^2}

$$\sqrt{ { 3000 }^{ 2 } - { 4000 }^{ 2 } }$$

Evaluate (complex solution)

$$1000\sqrt{7}i\approx 2645.751311065i$$

Solution Steps

Calculate 3000 to the power of 2 and get 9000000.

$$\sqrt{9000000-4000^{2}}$$

Calculate 4000 to the power of 2 and get 16000000.

$$\sqrt{9000000-16000000}$$

Subtract 16000000 from 9000000 to get -7000000.

$$\sqrt{-7000000}$$

Factor -7000000=\left(1000i\right)^{2}\times 7. Rewrite the square root of the product \sqrt{\left(1000i\right)^{2}\times 7} as the product of square roots \sqrt{\left(1000i\right)^{2}}\sqrt{7}. Take the square root of \left(1000i\right)^{2}.

$$1000i\sqrt{7}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$