Solve 4/2-sqrt{6}

$$\frac { 4 } { 2 - \sqrt { 6 } }$$

Evaluate

$$-2\sqrt{6}-4\approx -8.898979486$$

Solution Steps

Rationalize the denominator of \frac{4}{2-\sqrt{6}} by multiplying numerator and denominator by 2+\sqrt{6}.

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

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}.

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

Square 2. Square \sqrt{6}.

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

Subtract 6 from 4 to get -2.

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

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

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

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

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