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Why are number with even square roots always positive?

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cat2010
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Why are number with even square roots always positive? [#permalink] New post   29 Nov 2022, 04:16
Why are number with even square roots always positive?

Example : \(\sqrt{16}\) is 4 not -4
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divyadna
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Re: Why are number with even square roots always positive? [#permalink] New post   29 Nov 2022, 05:35
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√x^2= |x|

So, √4^2= |4|

But, √16= 4 OR -4

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TheWrongGrammer
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Re: Why are number with even square roots always positive? [#permalink] New post   29 Nov 2022, 06:04
cat2010 wrote:
Why are number with even square roots always positive?

Example : \(\sqrt{16}\) is 4 not -4



In GMAT
if the question stem says fine \sqrt{x} then value is always +x
But if
Question stem says find value of x such that
X^2 = 4 then x = +_ 2

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chetan2u
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Re: Why are number with even square roots always positive? [#permalink] New post   29 Nov 2022, 06:36
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divyadna wrote:
√x^2= |x|

So, √4^2= |4|

But, √16= 4 OR -4

Posted from my mobile device



That’s not correct.

In GMAT, we consider the positive value
So \(\sqrt{16}=4\).

While \(\sqrt{x^2}=|x|\), so x can surely be positive or negative, but the square root is absolute value of x, that is positive x.
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cat2010
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Re: Why are number with even square roots always positive? [#permalink] New post   29 Nov 2022, 09:53
chetan2u wrote:
divyadna wrote:
√x^2= |x|

So, √4^2= |4|

But, √16= 4 OR -4

Posted from my mobile device



That’s not correct.

In GMAT, we consider the positive value
So \(\sqrt{16}=4\).

While \(\sqrt{x^2}=|x|\), so x can surely be positive or negative, but the square root is absolute value of x, that is positive x.


chetan2u Can you please elaborate Red part ?
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gmatclubot
Re: Why are number with even square roots always positive? [#permalink]
29 Nov 2022, 09:53

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