Solve 1/sqrt{6-sqrt{4}}

$$\frac { 1 } { \sqrt { 6 } - \sqrt { 4 } }$$

Evaluate

$$\frac{\sqrt{6}}{2}+1\approx 2.224744871$$

Solution Steps

Calculate the square root of 4 and get 2.

$$\frac{1}{\sqrt{6}-2}$$

Rationalize the denominator of \frac{1}{\sqrt{6}-2} by multiplying numerator and denominator by \sqrt{6}+2.

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

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}.

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

Square \sqrt{6}. Square 2.

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

Subtract 4 from 6 to get 2.

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