Solve sqrt{(2-4)^2+(2sqrt{3}-0)^2}

$$\sqrt { ( 2 - 4 ) ^ { 2 } + ( 2 \sqrt { 3 } - 0 ) ^ { 2 } }$$

Evaluate

$$4$$

Solution Steps

Subtract 4 from 2 to get -2.

$$\sqrt{\left(-2\right)^{2}+\left(2\sqrt{3}-0\right)^{2}}$$

Calculate -2 to the power of 2 and get 4.

$$\sqrt{4+\left(2\sqrt{3}-0\right)^{2}}$$

Multiply -1 and 0 to get 0.

$$\sqrt{4+\left(2\sqrt{3}+0\right)^{2}}$$

Anything plus zero gives itself.

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

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

$$2^{2}$$