It is currently 26 Jun 2017, 19:35

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# |x| Absolute value property - general question

Author Message
TAGS:

### Hide Tags

Intern
Joined: 29 Aug 2012
Posts: 26
Schools: Babson '14
GMAT Date: 02-28-2013
|x| Absolute value property - general question [#permalink]

### Show Tags

30 Oct 2012, 04:58
1
This post was
BOOKMARKED
Is this true:

Range of values of |x| = x^2
and also |x| = sqrt. x^2
Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: |x| Absolute value property - general question [#permalink]

### Show Tags

30 Oct 2012, 05:55
himanshuhpr wrote:
Is this true:

Range of values of |x| = x^2
and also |x| = sqrt. x^2

Point 1 is not clear, what does the range of |x| mean?

As for $$\sqrt{x^2}=|x|$$.

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: |x| Absolute value property - general question   [#permalink] 30 Oct 2012, 05:55
Similar topics Replies Last post
Similar
Topics:
45 Properties of Absolute Values on the GMAT 6 24 Apr 2017, 01:47
2 X^2<x absolute value question 5 09 Oct 2012, 07:14
4 General questions about advanced absolute value questions 4 05 Feb 2016, 23:47
1 Absolute Value Question 6 22 Jan 2012, 08:57
Absolute value -- theory and questions 3 23 Aug 2010, 20:05
Display posts from previous: Sort by