Solve {left(2/sqrt{3-1}right)}^2-2/sqrt{3-1}+1

$${ \left( \frac{ 2 }{ \sqrt{ 3-1 } } \right) }^{ 2 } - \frac{ 2 }{ \sqrt{ 3-1 } } +1$$

Evaluate

$$3-\sqrt{2}\approx 1.585786438$$

Solution Steps

Subtract 1 from 3 to get 2.

$$\left(\frac{2}{\sqrt{2}}\right)^{2}-\frac{2}{\sqrt{3-1}}+1$$

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

$$\left(\frac{2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)^{2}-\frac{2}{\sqrt{3-1}}+1$$

The square of \sqrt{2} is 2.

$$\left(\frac{2\sqrt{2}}{2}\right)^{2}-\frac{2}{\sqrt{3-1}}+1$$

Cancel out 2 and 2.

$$\left(\sqrt{2}\right)^{2}-\frac{2}{\sqrt{3-1}}+1$$

The square of \sqrt{2} is 2.

$$2-\frac{2}{\sqrt{3-1}}+1$$

Subtract 1 from 3 to get 2.

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

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

Add 2 and 1 to get 3.

$$3-\sqrt{2}$$