Solve sqrt{4+{left(2sqrt{3}right)}^2}

$$\sqrt{ 4+ { \left(2 \sqrt{ 3 } \right) }^{ 2 } }$$

Evaluate

$$4$$

Solution Steps

Expand \left(2\sqrt{3}\right)^{2}.

$$\sqrt{4+2^{2}\left(\sqrt{3}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4+4\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{4+4\times 3}$$

Multiply 4 and 3 to get 12.

$$\sqrt{4+12}$$

Add 4 and 12 to get 16.

$$\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$4$$

Factor

$$2^{2}$$