$\begin{array}{l} a) \, 2\sqrt{{x}^2} = 2|x| = -2x \,\, với \,\, x <0\\ \dfrac{1}{2}\sqrt{{x^{10}}} = \dfrac{1}{2}.|x^5| = - \dfrac{1}{2}x^5 \,\,với\,\, x < 0\\ b)\,\sqrt{(a-5)^2} = |a-5| = 5 -a \,\,với\,\, a \leq5\\ \sqrt{(x-10)^{10}} = |(x-10)^5| = -(x - 10)^5 \,\,với \,\,x\leq 10\\ c)\,x -4 + \sqrt{x^2 - 8x + 16}\\ =x-4 + \sqrt{(x-4)^2}\\ =x-4 + |x-4|\\ = x - 4 - (x + 4) \,\,với \,\,x < 4\\ = -8\\ d)\,\sqrt{(\sqrt{x} - \sqrt{y})^2.(\sqrt{x} + \sqrt{y})^2}\\ =|\sqrt{x} - \sqrt{y}. |\sqrt{x} + \sqrt{y}|\\ = (\sqrt{y} - \sqrt{x}).(\sqrt{y} + \sqrt{x}) \,\,với\,\,0\leq x\leq y\\ =y - x \end{array}$