Solve -6/2-sqrt{2}

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

Evaluate

$$-3\sqrt{2}-6\approx -10.242640687$$

Solution Steps

Rationalize the denominator of \frac{-6}{2-\sqrt{2}} by multiplying numerator and denominator by 2+\sqrt{2}.

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

Consider \left(2-\sqrt{2}\right)\left(2+\sqrt{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Square 2. Square \sqrt{2}.

$$\frac{-6\left(2+\sqrt{2}\right)}{4-2}$$

Subtract 2 from 4 to get 2.

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

Divide -6\left(2+\sqrt{2}\right) by 2 to get -3\left(2+\sqrt{2}\right).

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

Use the distributive property to multiply -3 by 2+\sqrt{2}.

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