Solve (1-3sqrt{3})(2sqrt{6}-1)

$$( 1 - 3 \sqrt { 3 } ) ( 2 \sqrt { 6 } - 1 )$$

Evaluate

$$2\sqrt{6}+3\sqrt{3}-18\sqrt{2}-1\approx -16.360712214$$

Solution Steps

Apply the distributive property by multiplying each term of 1-3\sqrt{3} by each term of 2\sqrt{6}-1.

$$2\sqrt{6}-1-6\sqrt{3}\sqrt{6}+3\sqrt{3}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$2\sqrt{6}-1-6\sqrt{3}\sqrt{3}\sqrt{2}+3\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$2\sqrt{6}-1-6\times 3\sqrt{2}+3\sqrt{3}$$

Multiply -6 and 3 to get -18.

$$2\sqrt{6}-1-18\sqrt{2}+3\sqrt{3}$$