Solve (2+4sqrt{3})(6-sqrt{3})

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

Evaluate

$$22\sqrt{3}\approx 38.105117767$$

Solution Steps

Apply the distributive property by multiplying each term of 2+4\sqrt{3} by each term of 6-\sqrt{3}.

$$12-2\sqrt{3}+24\sqrt{3}-4\left(\sqrt{3}\right)^{2}$$

Combine -2\sqrt{3} and 24\sqrt{3} to get 22\sqrt{3}.

$$12+22\sqrt{3}-4\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$12+22\sqrt{3}-4\times 3$$

Multiply -4 and 3 to get -12.

$$12+22\sqrt{3}-12$$

Subtract 12 from 12 to get 0.

$$22\sqrt{3}$$