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M06-02

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singhall
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Re: M06-02 [#permalink] New post   28 Jun 2023, 22:59
Bunuel wrote:
rsamant wrote:
Why do we use absolute signs in this problem??


Because \(\sqrt{x^2}=|x|\). Check for more Absolute value tips: https://gmatclub.com/forum/absolute-val ... 75002.html


Theory on Abolute Values: https://gmatclub.com/forum/math-absolut ... 86462.html

DS Abolute Values Questions to practice: https://gmatclub.com/forum/search.php?s ... &tag_id=37
PS Abolute Values Questions to practice: https://gmatclub.com/forum/search.php?s ... &tag_id=58

Hope this helps.



What is the difference between Because \(\sqrt{x^2}=|x|\) and Mathematically the square root function cannot give negative result. When the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root.
I got the second explanation in a different question. https://gmatclub.com/forum/d01-183474.html

Even roots have only a positive value on the GMAT.

These two statements are creating a contradiction in my head. Can someone please help me clear the difference between these two?

Thanks!
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Bunuel
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Re: M06-02 [#permalink] New post   28 Jun 2023, 23:33
Expert Reply
singhall wrote:
Bunuel wrote:
rsamant wrote:
Why do we use absolute signs in this problem??


Because \(\sqrt{x^2}=|x|\). Check for more Absolute value tips: https://gmatclub.com/forum/absolute-val ... 75002.html


Theory on Abolute Values: https://gmatclub.com/forum/math-absolut ... 86462.html

DS Abolute Values Questions to practice: https://gmatclub.com/forum/search.php?s ... &tag_id=37
PS Abolute Values Questions to practice: https://gmatclub.com/forum/search.php?s ... &tag_id=58

Hope this helps.



What is the difference between Because \(\sqrt{x^2}=|x|\) and Mathematically the square root function cannot give negative result. When the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root.
I got the second explanation in a different question. https://gmatclub.com/forum/d01-183474.html

Even roots have only a positive value on the GMAT.

These two statements are creating a contradiction in my head. Can someone please help me clear the difference between these two?

Thanks!


What's causing the confusion? The square root symbol, or any even root such as the fourth root, cannot yield a negative result. Therefore, \(\sqrt{x^2}=|x|\), not simply x. This is because x can be negative, while |x| cannot.
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Re: M06-02 [#permalink] New post   29 Jun 2023, 11:35
Bunuel wrote:
singhall wrote:
Bunuel wrote:
Why do we use absolute signs in this problem??


Because \(\sqrt{x^2}=|x|\). Check for more Absolute value tips: https://gmatclub.com/forum/absolute-val ... 75002.html





What is the difference between Because \(\sqrt{x^2}=|x|\) and Mathematically the square root function cannot give negative result. When the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root.
I got the second explanation in a different question. https://gmatclub.com/forum/d01-183474.html

Even roots have only a positive value on the GMAT.

These two statements are creating a contradiction in my head. Can someone please help me clear the difference between these two?

Thanks!


What's causing the confusion? The square root symbol, or any even root such as the fourth root, cannot yield a negative result. Therefore, \(\sqrt{x^2}=|x|\), not simply x. This is because x can be negative, while |x| cannot.


Thanks for your response Bunuel
Okay, understood, I was confused because we were putting \(\sqrt{(y+1)^2}\) as |y+1| and not simply (y+1). Makes sense.
We can write \(\sqrt{y^2}\) as y but \(\sqrt{ (y+1)^2 } \) as |y+1| is so because y if less than -1 would yield a negative result.
Am I on the right track now?
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Re: M06-02 [#permalink] New post   05 Jul 2023, 00:43
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singhall wrote:
Bunuel wrote:
singhall wrote:
Because \(\sqrt{x^2}=|x|\). Check for more Absolute value tips: https://gmatclub.com/forum/absolute-val ... 75002.html





What is the difference between Because \(\sqrt{x^2}=|x|\) and Mathematically the square root function cannot give negative result. When the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root.
I got the second explanation in a different question. https://gmatclub.com/forum/d01-183474.html

Even roots have only a positive value on the GMAT.

These two statements are creating a contradiction in my head. Can someone please help me clear the difference between these two?

Thanks!


What's causing the confusion? The square root symbol, or any even root such as the fourth root, cannot yield a negative result. Therefore, \(\sqrt{x^2}=|x|\), not simply x. This is because x can be negative, while |x| cannot.


Thanks for your response Bunuel
Okay, understood, I was confused because we were putting \(\sqrt{(y+1)^2}\) as |y+1| and not simply (y+1). Makes sense.
We can write \(\sqrt{y^2}\) as y but \(\sqrt{ (y+1)^2 } \) as |y+1| is so because y if less than -1 would yield a negative result.
Am I on the right track now?


No. The following is always true: \(\sqrt{x^2}=|x|\).

For instance, of x = 5, then \(\sqrt{x^2}=|x|=5\) and if x = -5, then \(\sqrt{x^2}=|x|=5\).
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Re M06-02 [#permalink] New post   12 Aug 2023, 09:59
I think this is a high-quality question and I agree with explanation.
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Re M06-02 [#permalink]
12 Aug 2023, 09:59
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