If x =\((\sqrt5-\sqrt7)^2\), then the Best Approximation of x is GMAT Problem Solving

Question: If x = \((\sqrt5-\sqrt7)^2\), then the best approximation of x is:

1. 0
2. 1
3. 2
4. 3
5. 4

Correct Answer: A
Solution and Explanation:

There is only one approach to this problem.
Approach Solution 1:

Firstly, write the following expression:

x = \((\sqrt5-\sqrt7)^2\)

We will use the identity in this question:

\(x=(a-b)^2=a^2+b^2-2ab\)

Here in this question: a = \(\sqrt5\), b =\(\sqrt7\)

Hence solving this question, we will get:

\((\sqrt5-\sqrt7)^2=(\sqrt5)^2+(\sqrt7)^2-2*\sqrt5*\sqrt7\)
\((\sqrt5-\sqrt7)^2=(\sqrt5)^2+(\sqrt7)^2-2*\sqrt{35}\)

Since \(\sqrt{35}\approx6\), then \(12 - 2\sqrt{35}\approx12-2*6=0\)

“If x = \((\sqrt5-\sqrt7)^2\), then the best approximation of x is:”- 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. The candidates can solve GMAT Quant practice papers to improve their knowledge of mathematics.

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