Solve (1+2sqrt{3})(sqrt{3}+2)

$$( 1 + 2 \sqrt { 3 } ) ( \sqrt { 3 } + 2 )$$

Evaluate

$$5\sqrt{3}+8\approx 16.660254038$$

Solution Steps

Apply the distributive property by multiplying each term of 1+2\sqrt{3} by each term of \sqrt{3}+2.

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

The square of \sqrt{3} is 3.

$$\sqrt{3}+2+2\times 3+4\sqrt{3}$$

Multiply 2 and 3 to get 6.

$$\sqrt{3}+2+6+4\sqrt{3}$$

Add 2 and 6 to get 8.

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

Combine \sqrt{3} and 4\sqrt{3} to get 5\sqrt{3}.

$$5\sqrt{3}+8$$