Rounded to four decimal places, the square root of the

[BTGmoderatorLU]

Source: Manhattan Prep

Rounded to four decimal places, the square root of the square root of 0.9984 is approximately?

A. 0.9990
B. 0.9992
C. 0.9994
D. 0.9996
E. 0.9998

The OA is D

[Jay@ManhattanReview]

Source: Manhattan Prep

Rounded to four decimal places, the square root of the square root of 0.9984 is approximately?

A. 0.9990
B. 0.9992
C. 0.9994
D. 0.9996
E. 0.9998

The OA is D

So, we have to calculate the 4th root of 0.9984. Note that 0.9984 is less than 1 and square root or 4th root of a number less than 1 is GREATER than the number itself. Say x = 1/16 < 1. Thus, √x = √(1/16) = 1/4. Thus, √(1/4) = 1/2, greater than x = 1/16.

There are only two options that qualify: option D and E as they are greater than 0.9984, the number in the question narration.

Let's try with option D: If the square of the square of option D is equal to 0.9984, it is the correct answer, else option E.

Squaring the value of option D: 0.9996, we get (0.9996)^2 = (1 - 0.0004)^2 = 1 - 0.0008 + (0.0004)^2 = 0.9992 + a negligible number = ~0.9992

Again, squaring 0.9992, we get (0.9992)^2 = (1 - 0.0008)^2 = 1 - 0.0016 + + a negligible number = ~0.9984, equal to the number in question narration -- correct answer.

The correct answer: D

Hope this helps!

-Jay
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