Solve 1-sqrt{frac{2/2}}{sqrt{2/2}}-frac{1+sqrt{2}}{sqrt{2/2}}

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

Evaluate

$$-\left(\sqrt{2}+1\right)\approx -2.414213562$$

Solution Steps

Divide 2 by 2 to get 1.

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

Divide 2 by 2 to get 1.

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

Divide 2 by 2 to get 1.

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

Calculate the square root of 1 and get 1.

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

Subtract 1 from 1 to get 0.

$$\frac{0}{\sqrt{1}}-\frac{1+\sqrt{2}}{\sqrt{1}}$$

Calculate the square root of 1 and get 1.

$$\frac{0}{1}-\frac{1+\sqrt{2}}{\sqrt{1}}$$

Anything divided by one gives itself.

$$0-\frac{1+\sqrt{2}}{\sqrt{1}}$$

Calculate the square root of 1 and get 1.

$$0-\frac{1+\sqrt{2}}{1}$$

Anything divided by one gives itself.

$$0-\left(1+\sqrt{2}\right)$$

To find the opposite of 1+\sqrt{2}, find the opposite of each term.

$$0-1-\sqrt{2}$$

Subtract 1 from 0 to get -1.

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