Solve 8/2-sqrt{6}

$$\frac { 8 } { 2 - \sqrt { 6 } }$$

Evaluate

$$-4\sqrt{6}-8\approx -17.797958971$$

Solution Steps

Rationalize the denominator of \frac{8}{2-\sqrt{6}} by multiplying numerator and denominator by 2+\sqrt{6}.

$$\frac{8\left(2+\sqrt{6}\right)}{\left(2-\sqrt{6}\right)\left(2+\sqrt{6}\right)}$$

Consider \left(2-\sqrt{6}\right)\left(2+\sqrt{6}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{8\left(2+\sqrt{6}\right)}{2^{2}-\left(\sqrt{6}\right)^{2}}$$

Square 2. Square \sqrt{6}.

$$\frac{8\left(2+\sqrt{6}\right)}{4-6}$$

Subtract 6 from 4 to get -2.

$$\frac{8\left(2+\sqrt{6}\right)}{-2}$$

Divide 8\left(2+\sqrt{6}\right) by -2 to get -4\left(2+\sqrt{6}\right).

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

Use the distributive property to multiply -4 by 2+\sqrt{6}.

$$-8-4\sqrt{6}$$