Solve 2/(sqrt{2^2-1)4}

$$\frac { 2 } { ( \sqrt { 2 ^ { 2 } - 1 } ) 4 }$$

Evaluate

$$\frac{\sqrt{3}}{6}\approx 0.288675135$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{2}{4\sqrt{4-1}}$$

Subtract 1 from 4 to get 3.

$$\frac{2}{4\sqrt{3}}$$

Rationalize the denominator of \frac{2}{4\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{3}}{4\times 3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{3}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{\sqrt{3}}{6}$$