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Pokhran II
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Friends, is it safe to say that any square root, or cube 28 Nov 2006, 17:19
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Friends, is it safe to say that any square root, or cube root, or n-th root of a number that is greater than 1, is never be less than 1?

Please share your comments.

If that is true, then it is easier to reach an answer in this kind of question: https://www.gmatclub.com/phpbb/viewtopic.php?p=272590

In that link, M8 asked for formula to solve.

On the other hand, my assumption (Pokhran's Postulation :-D ) easily works out to nail the answer choice, which is E.

Or, is the assumption a mathematical blunder? Please comment.



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artshep
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Friends, is it safe to say that any square root, or cube 28 Nov 2006, 20:16
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I think the assumption is off.

For example, what about negative numbers?

4th root of 16 (a number greater than 1) is 2 and -2 (a number less than 1).
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Pokhran II
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Friends, is it safe to say that any square root, or cube 28 Nov 2006, 23:56
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artshep
I think the assumption is off.

For example, what about negative numbers?

4th root of 16 (a number greater than 1) is 2 and -2 (a number less than 1).
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Thanks! You have a point.

So, instead of saying ANY root, any POSITVE root is good.

"Any POSITIVE square root, cube root, or n-th root of a number that is greater than 1, is never be less than 1"
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tennis1ball
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Friends, is it safe to say that any square root, or cube 29 Nov 2006, 01:18
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It is not only safe. it is definite.

if n > 1, the any positive root is greater than 1.
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dwivedys
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Friends, is it safe to say that any square root, or cube 29 Nov 2006, 01:34
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tennis_ball
It is not only safe. it is definite.

if n > 1, the any positive root is greater than 1.
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That's because any number between 0 and 1 when raised to any POSITIVE Integral power can NEVER exceed 1 :-)

This means any positve number greater than 1 can never have a root whose absolute value is between 0 and 1.

Pokhran's postulate stands valid for all non-negative roots of a positive number greater than 1.
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Pokhran II
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Friends, is it safe to say that any square root, or cube 29 Nov 2006, 01:54
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tennis_ball
It is not only safe. it is definite.

if n > 1, the any positive root is greater than 1.
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dwivedys

This means any positve number greater than 1 can never have a root whose absolute value is between 0 and 1.

Pokhran's postulate stands valid for all non-negative roots of a positive number greater than 1.
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tennis_ball & dwivedys:
Thanks for the reassurance. Now I can confidently choose the best answer in the questions of such kind.



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