Simplify the following. 
​$$\left[ \left(1 - \frac{1}{2}\right)\left(1 - \frac{1}{3}\right)\left(1 - \frac{1}{4}\right) \cdots \left(1 - \frac{1}{100}\right) \right]^{-0.5}$$​​

Correct option is D

Given:
​$$\left[ \left(1 - \frac{1}{2}\right)\left(1 - \frac{1}{3}\right)\left(1 - \frac{1}{4}\right) \cdots \left(1 - \frac{1}{100}\right) \right]^{-0.5}$$​​
Formula Used:
The formula used for simplifying the individual terms is:
​$$1 - \frac1n = \frac{n - 1}n$$​​
Solution:
$$= \left[ \left(1 - \frac{1}{2}\right)\left(1 - \frac{1}{3}\right)\left(1 - \frac{1}{4}\right) \cdots \left(1 - \frac{1}{100}\right) \right]^{-0.5} \\\ \\ = \left[ \left( \frac{2-1}{2}\right)\left( \frac{3-1}{3}\right)\left( \frac{4-1}{4}\right) \cdots \left(\frac{100- 1 }{100}\right) \right]^{-0.5}$$​​​
​$$= \left[ \left( \frac{1}{2} \right) \times \left( \frac{2}{3} \right) \times \left( \frac{3}{4} \right) \times \cdots \times \left( \frac{99}{100} \right) \right]^{-0.5}\\= \left( \frac{1}{100} \right)^{-0.5}\\ = \sqrt{100} = 10$$

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