Simplifying $f(\sqrt{7})$, where $f(x) = \sqrt{x-4\sqrt{x-4}}+\sqrt{x+4\sqrt{x-4}}$

Set $\sqrt{x-4}=u \to x=u^2+4\\$so $$\sqrt{x-4\sqrt{x-4}}+\sqrt{x+4\sqrt{x-4}}=\\ \sqrt{u^2+4-4u}+\sqrt{u^2+4+4u}=\\ |u-2|+|u+2|=\\ |\sqrt{x-4}-2|+|\sqrt{x-4}+2|$$ but when deals to imaginary numbers absolute sign is not necessary.

Tags:

Complex Numbers

Functions

Algebra Precalculus

Nested Radicals

Rationalising Denominator

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