Solve 2/sqrt{2+sqrt{7-7}}

$$\frac{ 2 }{ \sqrt{ 2 } + \sqrt{ 7-7 } }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Subtract 7 from 7 to get 0.

$$\frac{2}{\sqrt{2}+\sqrt{0}}$$

Calculate the square root of 0 and get 0.

$$\frac{2}{\sqrt{2}+0}$$

Anything plus zero gives itself.

$$\frac{2}{\sqrt{2}}$$

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

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

The square of \sqrt{2} is 2.

$$\frac{2\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$\sqrt{2}$$