Solve (sqrt{6}-1)(sqrt{6}+2)-sqrt{18}

$$( \sqrt { 6 } - 1 ) ( \sqrt { 6 } + 2 ) - \sqrt { 18 }$$

Evaluate

$$\sqrt{6}+4-3\sqrt{2}\approx 2.206849056$$

Solution Steps

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

$$\left(\sqrt{6}\right)^{2}+2\sqrt{6}-\sqrt{6}-2-\sqrt{18}$$

The square of \sqrt{6} is 6.

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

Combine 2\sqrt{6} and -\sqrt{6} to get \sqrt{6}.

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

Subtract 2 from 6 to get 4.

$$4+\sqrt{6}-\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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