Solve (sqrt{6}-1)(sqrt{6}+2)-frac{sqrt{18}}{sqrt{3}}

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

Evaluate

$$4$$

Solution Steps

Rewrite the division of square roots \frac{\sqrt{18}}{\sqrt{3}} as the square root of the division \sqrt{\frac{18}{3}} and perform the division.

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

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

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

The square of \sqrt{6} is 6.

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

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

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

Subtract 2 from 6 to get 4.

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

Subtract \sqrt{6} from \sqrt{6} to get 0.

$$4$$

Factor

$$2^{2}$$