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

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

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

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

$$6+4\sqrt{3}-3\sqrt{3}-2\left(\sqrt{3}\right)^{2}$$

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

$$6+\sqrt{3}-2\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$6+\sqrt{3}-2\times 3$$

Multiply -2 and 3 to get -6.

$$6+\sqrt{3}-6$$

Subtract 6 from 6 to get 0.

$$\sqrt{3}$$