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

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

Evaluate

$$-2\sqrt{2}-3\approx -5.828427125$$

Solution Steps

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

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 2 and -1 to get -2.

$$-\sqrt{2}-1-2-\sqrt{2}$$

Subtract 2 from -1 to get -3.

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

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

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