Solve =sqrt{(2sqrt{2})^2-(sqrt{2})^2}

$$= \sqrt { ( 2 \sqrt { 2 } ) ^ { 2 } - ( \sqrt { 2 } ) ^ { 2 } }$$

Evaluate

$$\sqrt{6}\approx 2.449489743$$

Solution Steps

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{2} is 2.

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

Multiply 4 and 2 to get 8.

$$\sqrt{8-\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{8-2}$$

Subtract 2 from 8 to get 6.

$$\sqrt{6}$$