Hi All,
This question is a tricky Gmat prep question, which i got wrong can anyone help me to get the right answer. Will highly appreciate a quick reply.
If X<0 then find square root of [-X. Modulus X]
Thanks
Abhinav
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Its simply [-X]
to visulalize yourself pls take x=-5 and proceed.
to visulalize yourself pls take x=-5 and proceed.
If you feel like it, hit thanks
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- cypherskull
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If I understand the ques correctly, we need to find sq. root of -X times |X|.
I think the answer would be X.
If X<0, -X would be a positive term. -X times |X| = X^2. Hence the sq. root would be X.
I think the answer would be X.
If X<0, -X would be a positive term. -X times |X| = X^2. Hence the sq. root would be X.
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yes u did understand the ques correctly. i also found the same answer but OA is -X.... hw? don't know
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Hi Abhinav,
This is an important concept. And when one first comes around it, it seems a little difficult to digest.
Let's try to understand this.
First of all: By definition the square root of any Quantity is a positive number. Always!
If x > 0,
x^2 > 0.
square root(x^2) = x (a positive number)
But if x < 0,
x^2 > 0
While taking the square root of x^2 now we have to keep in mind that square root(x^2) should be a positive number.
So, if square root(x^2) = x, then it's negative because x is negative.
To respect the definition of square root, a '-1' is multiplied to x to retain the value but change the sign.
now,
square root(x^2) = -x (which is a positive number. Isn't it?)
Thus
square root(x^2) = x when x > 0
square root(x^2) = -x when x < 0.
If you notice, this is same as the definition of modulus, which states that
|x| = x when x > 0
|x| = -x when x < 0.
To put the definition of square root(x^2) concisely
square root(x^2) = |x|
This is an important concept. And when one first comes around it, it seems a little difficult to digest.
Let's try to understand this.
First of all: By definition the square root of any Quantity is a positive number. Always!
If x > 0,
x^2 > 0.
square root(x^2) = x (a positive number)
But if x < 0,
x^2 > 0
While taking the square root of x^2 now we have to keep in mind that square root(x^2) should be a positive number.
So, if square root(x^2) = x, then it's negative because x is negative.
To respect the definition of square root, a '-1' is multiplied to x to retain the value but change the sign.
now,
square root(x^2) = -x (which is a positive number. Isn't it?)
Thus
square root(x^2) = x when x > 0
square root(x^2) = -x when x < 0.
If you notice, this is same as the definition of modulus, which states that
|x| = x when x > 0
|x| = -x when x < 0.
To put the definition of square root(x^2) concisely
square root(x^2) = |x|
Aneesh Bangia
GMAT Math Coach
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GMATPad:
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GMAT Math Coach
[email protected]
GMATPad:
Facebook Page: https://www.facebook.com/GMATPad