GMAT Prep is not just about books. To prepare right, you must learn to look beyond the bookish concepts. In this series of short articles, I am going to talk about some interesting concepts which ScoreChase GMAT covers comprehensively in their courses but most books miss.
What is the difference between √x and (x)^1/2 ?
This is a very critical concept. There is a very crucial difference
√x : √ sign (the radical sign) is called the “Principal root” and always results in a non-negative number.
(x)^1/2: The x to the power of 1/2 is the result of the equation, y^2 = x. In this case the result could be “positive or negative or zero”.
So here is the conclusion
√x : Always non-negative
(x)^1/2: Can be positive or negative or zero
As in ScoreChase GMAT Workshops, we don’t believe a concept is complete without working on an example. Here is a question that will help you understand this topic a little bit better:
Q. For a negative integer x, what is the value of x * √(x^2) ?
A) x^2
B) -x^2
C) x
D) -x
E) -1
Once you have found an answer. Please highlight the text below to see the solution
________________________
Since x is negative, -x will be positive
Since √(x^2) yields positive result and x is negative, the result will be -x
So, x*√(x^2) = x * -x = -x^2
(B)
________________________
Simple enough!
Stay tuned for more beyond the book concepts !
About ScoreChase:
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a creative way to write the answer….good.