Solve 1000^2+(400sqrt{2})^2-32000

$$1000 ^ { 2 } + ( 400 \sqrt { 2 } ) ^ { 2 } - 32000$$

Evaluate

$$1288000$$

Solution Steps

Calculate 1000 to the power of 2 and get 1000000.

$$1000000+\left(400\sqrt{2}\right)^{2}-32000$$

Expand \left(400\sqrt{2}\right)^{2}.

$$1000000+400^{2}\left(\sqrt{2}\right)^{2}-32000$$

Calculate 400 to the power of 2 and get 160000.

$$1000000+160000\left(\sqrt{2}\right)^{2}-32000$$

The square of \sqrt{2} is 2.

$$1000000+160000\times 2-32000$$

Multiply 160000 and 2 to get 320000.

$$1000000+320000-32000$$

Add 1000000 and 320000 to get 1320000.

$$1320000-32000$$

Subtract 32000 from 1320000 to get 1288000.

$$1288000$$

Factor

$$2^{6}\times 5^{3}\times 7\times 23$$