Solve 1/sqrt{6-sqrt{5}}

$$\frac { 1 } { \sqrt { 6 } - \sqrt { 5 } }$$

Evaluate

$$\sqrt{5}+\sqrt{6}\approx 4.68555772$$

Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{6}-\sqrt{5}} by multiplying numerator and denominator by \sqrt{6}+\sqrt{5}.

$$\frac{\sqrt{6}+\sqrt{5}}{\left(\sqrt{6}-\sqrt{5}\right)\left(\sqrt{6}+\sqrt{5}\right)}$$

Consider \left(\sqrt{6}-\sqrt{5}\right)\left(\sqrt{6}+\sqrt{5}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\sqrt{6}+\sqrt{5}}{\left(\sqrt{6}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

Square \sqrt{6}. Square \sqrt{5}.

$$\frac{\sqrt{6}+\sqrt{5}}{6-5}$$

Subtract 5 from 6 to get 1.

$$\frac{\sqrt{6}+\sqrt{5}}{1}$$

Anything divided by one gives itself.

$$\sqrt{6}+\sqrt{5}$$