Solve sqrt{(2sqrt{5})^2-(2)^2}

$$\sqrt { ( 2 \sqrt { 5 } ) ^ { 2 } - ( 2 ) ^ { 2 } }$$

Evaluate

$$4$$

Solution Steps

Expand \left(2\sqrt{5}\right)^{2}.

$$\sqrt{2^{2}\left(\sqrt{5}\right)^{2}-2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4\left(\sqrt{5}\right)^{2}-2^{2}}$$

The square of \sqrt{5} is 5.

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

Multiply 4 and 5 to get 20.

$$\sqrt{20-2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{20-4}$$

Subtract 4 from 20 to get 16.

$$\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$4$$

Factor

$$2^{2}$$