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1. $[8 - {(\frac{4^{\frac{9}{4}} \sqrt{{2.2}^{2}}}{2 \sqrt{2^{- 2}}})}^{^{\frac{1}{2}}}]$ is equal to = ?

A. 32

B. 8

C. 1

D. 0

Solution:

\begin{aligned} [8 - {(\frac{4^{\frac{9}{4}} \sqrt{{2.2}^{2}}}{2 \sqrt{2^{- 2}}})}^{^{\frac{1}{2}}}] \\ = [8 - {(\frac{2^{2 \times \frac{9}{4}} \sqrt{2^{1 + 2}}}{2 \sqrt{\frac{1}{4}}})}^{^{\frac{1}{2}}}] \\ = [8 - {(\frac{2^{\frac{9}{2}} {.2}^{\frac{3}{2}}}{2 \times \frac{1}{2}})}^{^{\frac{1}{2}}}] \\ = [8 - {(2^{\frac{12}{2}})}^{^{\frac{1}{2}}}] \\ = [8 - (2^{6 \times \frac{1}{2}})] \\ = [8 - (2^{3})] \\ = [8 - 8] \\ = 0 \end{aligned}

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