Solve (6-sqrt{3})(1+sqrt{3})

$$( 6 - \sqrt { 3 } ) ( 1 + \sqrt { 3 } )$$

Evaluate

$$5\sqrt{3}+3\approx 11.660254038$$

Solution Steps

Apply the distributive property by multiplying each term of 6-\sqrt{3} by each term of 1+\sqrt{3}.

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

Combine 6\sqrt{3} and -\sqrt{3} to get 5\sqrt{3}.

$$6+5\sqrt{3}-\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$6+5\sqrt{3}-3$$

Subtract 3 from 6 to get 3.

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