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# Going thru the beginning chapters from GMAT Math book v3, it reads:

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Manager
Joined: 30 May 2012
Posts: 208
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Going thru the beginning chapters from GMAT Math book v3, it reads:  [#permalink]

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24 May 2017, 14:19
Going thru the beginning chapters from GMAT Math book v3, it reads:
$$\sqrt{x^2}$$ = |x| and
when x<=0 then $$\sqrt{x^2}$$ = -x and
when x>= 0 then $$\sqrt{x^2}$$ = x.

My Math is rusty but don't you have to square both sides in order to remove the modulus? Pardon my ignorance on the topic. Maybe someone could help me understand the concept?

p.s: I did search for this question before I posted but the search yielded no results due to too many common parameters provided.
Current Student
Joined: 18 Jan 2017
Posts: 81
Location: India
Concentration: Finance, Economics
GMAT 1: 700 Q50 V34
Going thru the beginning chapters from GMAT Math book v3, it reads:  [#permalink]

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24 May 2017, 18:01
Look at it this way,

$$(-2)^2=4$$
$$(2)^2=4$$

Hence applying the reverse
$$√4 =2 or -2$$

and 2 and -2 can be collectively referred as |2|

Thus it follows
$$x^2 = |x|$$and
when $$x<=0$$then $$x^2−−√x2 = -x$$ and
when $$x>= 0$$then $$x^2−−√x2 = x$$.

This is a very powerful concept, used in multiple questions you will see on this forum. You can check the absolute value/modulus tags for this
https://gmatclub.com/forum/search.php?s ... &tag_id=37
Manager
Joined: 30 May 2012
Posts: 208
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Re: Going thru the beginning chapters from GMAT Math book v3, it reads:  [#permalink]

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25 May 2017, 14:47
Tan2017 wrote:
Look at it this way,

...

Thus it follows
$$x^2 = |x|$$and
when $$x<=0$$then $$x^2−−√x2 = -x$$ and
when $$x>= 0$$then $$x^2−−√x2 = x$$.

...

I followed you until $$x^2 = |x|$$ ... LOL. I am not sure I understood what followed after. Could you dumb it down a notch for me, please?
Math Expert
Joined: 02 Sep 2009
Posts: 52164
Re: Going thru the beginning chapters from GMAT Math book v3, it reads:  [#permalink]

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25 May 2017, 14:52
Blackbox wrote:
Going thru the beginning chapters from GMAT Math book v3, it reads:
$$\sqrt{x^2}$$ = |x| and
when x<=0 then $$\sqrt{x^2}$$ = -x and
when x>= 0 then $$\sqrt{x^2}$$ = x.

My Math is rusty but don't you have to square both sides in order to remove the modulus? Pardon my ignorance on the topic. Maybe someone could help me understand the concept?

p.s: I did search for this question before I posted but the search yielded no results due to too many common parameters provided.

MUST KNOW: $$\sqrt{x^2}=|x|$$:

The point here is that since square root function cannot give negative result then $$\sqrt{some \ expression}\geq{0}$$.

So $$\sqrt{x^2}\geq{0}$$. But what does $$\sqrt{x^2}$$ equal to?

Let's consider following examples:
If $$x=5$$ --> $$\sqrt{x^2}=\sqrt{25}=5=x=positive$$;
If $$x=-5$$ --> $$\sqrt{x^2}=\sqrt{25}=5=-x=positive$$.

So we got that:
$$\sqrt{x^2}=x$$, if $$x\geq{0}$$;
$$\sqrt{x^2}=-x$$, if $$x<0$$.

What function does exactly the same thing? The absolute value function: $$|x|=x$$, if $$x\geq{0}$$ and $$|x|=-x$$, if $$x<0$$. That is why $$\sqrt{x^2}=|x|$$.

Hope it's clear.
_________________
Re: Going thru the beginning chapters from GMAT Math book v3, it reads: &nbs [#permalink] 25 May 2017, 14:52
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