Reducing square root expression

Let $ a,b\in N $ such as $ a^2-b=c^2 $ for some $ c\in N $ Then

$$ \sqrt{a\pm \sqrt b}=\sqrt{\frac{a+c}{2}}\pm \sqrt{\frac{a-c}{2}}$$

It is easy to verify as

$$a\pm \sqrt b=\frac{a+c}{2}}+\frac{a-c}{2}\pm 2\sqrt{\frac{a^2-c^2}{4}}=a\pm \sqrt b$$

An example :for a=2 and b=3 we have c=1 so

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

a=6 and b=11 we have $ c^2=36-11=25 $ so $ c=5 $

$$ \sqrt{6\pm \sqrt 11}=\sqrt{\frac{6+5}{2}}\pm \sqrt{\frac{6-5}{2}}=\sqrt{\frac{11}{2}}\pm \sqrt{\frac{1}{2}}$$
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