For a Negative Integer x, What is the Value of \(x*\sqrt{(x^2)}\)? GMAT Problem Solving

Question: For a negative integer x, what is the value of x * √(x²)?  

A) x²
B) -x²
C) x
D) -x
E) -1

Answer: B

Solution and Explanation:

Approach Solution 1:
To answer this GMAT question, apply the data provided in the question. These issues pertain to many different branches of mathematics. This query relates to algebra. Because of how the options are set up, it is hard to choose the best one. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
It is asked in the question to find out the value of x * √(x²) where x is negative
√x: This sign (the radical sign) always yields a non-negative number.
(x)^1/2: The answer to the equation y² = x is (x) to the power of 1/2. A "positive, negative, or zero" outcome is possible in this situation.
Therefore, this is the judgment:
√x: Note that it is not said that it's always "positive"; it's always non-negative.
(x)^1/2: either a positive, negative, or zero value
Correct option: B

Approach Solution 2:
To answer this GMAT question, apply the data provided in the question. These issues pertain to many different branches of mathematics. This query relates to algebra. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
It is asked in the question to find out the value of x * √(x²) where x is negative
According to the above notes: x < 0
x∗√(x²) = x∗|x|
|x| = -x if x is negative and x if x is positive
Here x is negative
|x| = -x
We get x*(-x) = -x²
Let us take an example,
X = -2
-2 * √((-2)²) = -2 *√(4) = -2 * (2) = -4
Correct option: B

Approach Solution 3:
To answer this GMAT question, apply the data that was provided in the question. These issues pertain to many different branches of mathematics. This query relates to algebra. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
It is asked in the question to find out the value of x * √(x²) where x is negative
For any negative integer x, we have:
x * √(x²) = x * |x| = (-|x|) * |x| = -|x|²
Therefore, the value of x * √(x²) for any negative integer x is -|x|².
Correct option: B

“For a negative integer x, what is the value of x*root(x²)?" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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