Solve sqrt{25^2-{left(4sqrt{6}right)}^2}

$$\sqrt{ { 25 }^{ 2 } - { \left(4 \sqrt{ 6 } \right) }^{ 2 } }$$

Evaluate

$$23$$

Solution Steps

Calculate 25 to the power of 2 and get 625.

$$\sqrt{625-\left(4\sqrt{6}\right)^{2}}$$

Expand \left(4\sqrt{6}\right)^{2}.

$$\sqrt{625-4^{2}\left(\sqrt{6}\right)^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{625-16\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\sqrt{625-16\times 6}$$

Multiply 16 and 6 to get 96.

$$\sqrt{625-96}$$

Subtract 96 from 625 to get 529.

$$\sqrt{529}$$

Calculate the square root of 529 and get 23.

$$23$$

Factor

$$23$$