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If ((x+4)^2)^1/2=3, which of the following could be the

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If \(\sqrt{(x+4)^2} = 3\), which of the following could be the value of x - 4?

A. -11
B. -7
C. -4
D. -3
E. 5

I am confused the way this was solved. Please provide your details solutions, post which I will post my specific question.
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Dec 2012, 01:07, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If ((x+4)^2)^1/2=3, which of the following could be the [#permalink]

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New post 10 Dec 2012, 01:11
If \(\sqrt{(x+4)^2} = 3\), which of the following could be the value of x - 4?

A. -11
B. -7
C. -4
D. -3
E. 5

\(\sqrt{(x+4)^2} = 3\) --> \((x+4)^2=9\) --> \(x+4=3\) or \(x+4=-3\) --> \(x=-1\) or \(x=-7\) --> \(x-4=-5\) or \(x-4=-11\).

Answer: A.

Hope it's clear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Please pay attention to the rule #3. Thank you.
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Re: If ((x+4)^2)^1/2=3, which of the following could be the [#permalink]

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New post 10 Dec 2012, 01:33
Bunuel wrote:
If \(\sqrt{(x+4)^2} = 3\), which of the following could be the value of x - 4?

A. -11
B. -7
C. -4
D. -3
E. 5

\(\sqrt{(x+4)^2} = 3\) --> \((x+4)^2=9\) --> \(x+4=3\) or \(x+4=-3\) --> \(x=-1\) or \(x=-7\) --> \(x-4=-5\) or \(x-4=-11\).

Answer: A.

Hope it's clear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Please pay attention to the rule #3. Thank you.


Bunuel, at 1st place why are you squaring both sides when we know that square root have a value of 1/2 which eventually cancels out the square.
\sqrt{(x+4)^2=3}
so this leaves me with x+4=3
and x=-1.
What is wrong with my approach. I know that I don't have an option of -5 in the answer but still my solution is correct.
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Re: If ((x+4)^2)^1/2=3, which of the following could be the [#permalink]

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New post 10 Dec 2012, 01:43
davidfrank wrote:
Bunuel wrote:
If \(\sqrt{(x+4)^2} = 3\), which of the following could be the value of x - 4?

A. -11
B. -7
C. -4
D. -3
E. 5

\(\sqrt{(x+4)^2} = 3\) --> \((x+4)^2=9\) --> \(x+4=3\) or \(x+4=-3\) --> \(x=-1\) or \(x=-7\) --> \(x-4=-5\) or \(x-4=-11\).

Answer: A.

Hope it's clear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Please pay attention to the rule #3. Thank you.


Bunuel, at 1st place why are you squaring both sides when we know that square root have a value of 1/2 which eventually cancels out the square.
\sqrt{(x+4)^2=3}
so this leaves me with x+4=3
and x=-1.
What is wrong with my approach. I know that I don't have an option of -5 in the answer but still my solution is correct.


That's not correct.

\(\sqrt{x^2} =|x|\) (check here: if-x-3-4-and-y-2-5-what-is-the-value-of-110071.html#p880130), thus \(\sqrt{(x+4)^2} =|x+4|\) not x+4.

From \(|x+4|=3\) --> \(x=-1\) or \(x=-7\).

Hope it's clear.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If ((x+4)^2)^1/2=3, which of the following could be the [#permalink]

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New post 10 Dec 2012, 03:44
Ans: Squaring both the sides we get (x+4)^2=9, therefore (x+4)=3,-3. So (x-4) could be -5 or -11. The answer is (A).
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Re: If ((x+4)^2)^1/2=3, which of the following could be the [#permalink]

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