Question: For a negative integer x, what is the value of x * √(x^2)?
- x^2
- -x^2
- x
- -x
- -1
“For a negative integer x, what is the value of x * √(x^2)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “The Official Guide for GMAT Reviews”. 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.
Solution and Explanation:
Approach Solution 1:
This question has only one approach.
It is given in the question that x is a negative integer, it is asked to find out the value of x * √(x^2)?
Given x < 0
Given expression
x*√(x^2)
It should be noted that \(\sqrt{x^2}\) = |x|
According to the above notes: x∗ \(\sqrt{x^2}\) => x∗|x|, since x<0 then |x|=−x
X∗|x| = x ∗ (−x) = -\(x^2\)
So we get,
x*√(x^2) = x * |x|
We are given that the value of x < 0
Or just substitute some negative x, let x=−2 < 0
x=−2 < 0 --> (−2)(\(\sqrt{(-2)^2}\) =(−2)∗\(\sqrt{4}\) = −2 * 2 = −4
We get,|
x*√(x^2) = x * |x| = x*(-x) = -\(x^2\)
Correct Answer: B
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