Solve sqrt{2}+frac{sqrt{2}}{sqrt{(sqrt{2})^2-1}}

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

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

The square of \sqrt{2} is 2.

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

Subtract 1 from 2 to get 1.

$$\sqrt{2}+\frac{\sqrt{2}}{\sqrt{1}}$$

Calculate the square root of 1 and get 1.

$$\sqrt{2}+\frac{\sqrt{2}}{1}$$

Anything divided by one gives itself.

$$\sqrt{2}+\sqrt{2}$$

Combine \sqrt{2} and \sqrt{2} to get 2\sqrt{2}.

$$2\sqrt{2}$$