Solve sqrt{240^2-{left(160sqrt{2}right)}^2}

$$\sqrt{ { 240 }^{ 2 } - { \left(160 \sqrt{ 2 } \right) }^{ 2 } }$$

Evaluate

$$80$$

Solution Steps

Calculate 240 to the power of 2 and get 57600.

$$\sqrt{57600-\left(160\sqrt{2}\right)^{2}}$$

Expand \left(160\sqrt{2}\right)^{2}.

$$\sqrt{57600-160^{2}\left(\sqrt{2}\right)^{2}}$$

Calculate 160 to the power of 2 and get 25600.

$$\sqrt{57600-25600\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{57600-25600\times 2}$$

Multiply 25600 and 2 to get 51200.

$$\sqrt{57600-51200}$$

Subtract 51200 from 57600 to get 6400.

$$\sqrt{6400}$$

Calculate the square root of 6400 and get 80.

$$80$$

Factor

$$2^{4}\times 5$$