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

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

Evaluate

$$3\sqrt{3}+9-\sqrt{6}-3\sqrt{2}\approx 7.504021993$$

Solution Steps

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

$$9-3\sqrt{2}+3\sqrt{3}-\sqrt{3}\sqrt{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$9-3\sqrt{2}+3\sqrt{3}-\sqrt{6}$$

Factor

$$3 \sqrt{3} + 9 - \sqrt{6} - 3 \sqrt{2} = 7.504021993$$