Solve frac{(sqrt{2}-1)*(frac{2-sqrt{2}}{2})}{2}

$$\frac { ( \sqrt { 2 } - 1 ) \times ( \frac { 2 - \sqrt { 2 } } { 2 } ) } { 2 }$$

Evaluate

$$\frac{3\sqrt{2}}{4}-1\approx 0.060660172$$

Solution Steps

Express \left(\sqrt{2}-1\right)\times \frac{2-\sqrt{2}}{2} as a single fraction.

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

Express \frac{\frac{\left(\sqrt{2}-1\right)\left(2-\sqrt{2}\right)}{2}}{2} as a single fraction.

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

Multiply 2 and 2 to get 4.

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

Apply the distributive property by multiplying each term of \sqrt{2}-1 by each term of 2-\sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Subtract 2 from -2 to get -4.

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

Combine 2\sqrt{2} and \sqrt{2} to get 3\sqrt{2}.

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

Factor

$$\frac{3 \sqrt{2} - 4}{4} = 0.060660171779821415$$