I have the following formula which I suspect I may be able to reduce further but I haven't found a way yet. Is there is method I can follow to ensure that I have reached the simplest form possible?
$$\sqrt{1 - \frac{2 - \sqrt{2}}{4}}$$
Generally when I go to reduce something I just play around with the numbers until my brain, through some process unknown to me, realizes that something can be simplified by doing XYZ thing. For example:
$$\sqrt{\Bigg(\frac{\sqrt{2}}{2}\Bigg)^2 + \Bigg(1 - \frac{\sqrt{2}}{2}\Bigg)^2}$$ $$\sqrt{\Bigg(\frac{\sqrt{2}}{\sqrt{4}}\Bigg)^2 + \Bigg(1 - \frac{\sqrt{2}}{2}\Bigg)\Bigg(1 - \frac{\sqrt{2}}{2}\Bigg)}$$ $$\sqrt{\frac{2}{4} + 1 - 2\frac{\sqrt{2}}{2} + \frac{2}{4}}$$ $$\sqrt{\frac{1}{2} + 1 - \sqrt{2} + \frac{1}{2}}$$ $$\sqrt{2 - \sqrt{2}}$$
The question again:
Is there is method I can follow to ensure that I have reached the simplest form possible?
Basically, is there a way to make sure that I have covered all the bases?