(C) Given expression is $\sqrt{(\log_{0.5} 4)^2}$.We know that $\sqrt{x^2} = |x|$.So,$\sqrt{(\log_{0.5} 4)^2} = |\log_{0.5} 4|$.We can write $0.5$ as

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(C) Given expression is $\sqrt{(\log_{0.5} 4)^2}$.We know that $\sqrt{x^2} = |x|$.So,$\sqrt{(\log_{0.5} 4)^2} = |\log_{0.5} 4|$.We can write $0.5$ as $2^{-1}$ and $4$ as $2^2$.Thus,$\log_{0.5} 4 = \log_{2^{-1}} (2^2)$.Using the property $\log_{a^n} (b^m) = \frac{m}{n} \log_a b$,we get $\frac{2}{-1} \log_2 2 = -2 \times 1 = -2$.Therefore,$|-2| = 2$.