Solve 2/sqrt{6+2}

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

Evaluate

$$\sqrt{6}-2\approx 0.449489743$$

Solution Steps

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

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

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

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

Square \sqrt{6}. Square 2.

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

Subtract 4 from 6 to get 2.

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

Cancel out 2 and 2.

$$\sqrt{6}-2$$