If n = √{16/81} , what is the value of √n GMAT Problem Solving

Question: If n = \(√{16/81}\) \(\) what is the value of √n GMAT Problem Solving ?

     A. 1/9
     B. 1/4
     C. 4/9
     D. 2/3
     E. 9/2

Answer: D

Approach Solution (1):
We have n = (16/81)^(1/2) = (4²/9²)^(1/2) = 4/9
n^(1/2) = (4/9)^(1/2)
n^(1/2) = (2²/3²)^^(1/2) = 2/3
Correct option: D

Approach Solution (2):
Note also that when you take the root of a fraction between 0 and 1, the value of the fraction increases and moves closer to 1.
If n = 4/9, then √ (4/9) must be between 4/9 and 1. The only value in that range is 2/3
Correct option: D

Approach Solution (3):
When taking the square root of a fraction, you must take the square root of the numerator and the square root of the denominator.
Here, the square root of 16/81 = 4/9
We're then asked to calculate the square root of 4/9.... and that would be 2/3
Correct option: D

“If n = \(√{16/81}\), what is the value of ? √n ?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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