Solve 6/sqrt{10-2}

$$\frac { 6 } { \sqrt { 10 } - 2 }$$

Evaluate

$$\sqrt{10}+2\approx 5.16227766$$

Solution Steps

Rationalize the denominator of \frac{6}{\sqrt{10}-2} by multiplying numerator and denominator by \sqrt{10}+2.

$$\frac{6\left(\sqrt{10}+2\right)}{\left(\sqrt{10}-2\right)\left(\sqrt{10}+2\right)}$$

Consider \left(\sqrt{10}-2\right)\left(\sqrt{10}+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}.

$$\frac{6\left(\sqrt{10}+2\right)}{\left(\sqrt{10}\right)^{2}-2^{2}}$$

Square \sqrt{10}. Square 2.

$$\frac{6\left(\sqrt{10}+2\right)}{10-4}$$

Subtract 4 from 10 to get 6.

$$\frac{6\left(\sqrt{10}+2\right)}{6}$$

Cancel out 6 and 6.

$$\sqrt{10}+2$$