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

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

Evaluate

$$4\sqrt{3}+7\approx 13.92820323$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2-\sqrt{3}\right)^{2}.

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

The square of \sqrt{3} is 3.

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

Add 4 and 3 to get 7.

$$7-4\sqrt{3}-4\left(-2\right)\sqrt{3}$$

Multiply 4 and -2 to get -8.

$$7-4\sqrt{3}-\left(-8\sqrt{3}\right)$$

The opposite of -8\sqrt{3} is 8\sqrt{3}.

$$7-4\sqrt{3}+8\sqrt{3}$$

Combine -4\sqrt{3} and 8\sqrt{3} to get 4\sqrt{3}.

$$7+4\sqrt{3}$$