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

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

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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

Originally posted by davidfrank on 10 Dec 2012, 01:58.
Last edited by Bunuel on 25 Dec 2017, 22:55, edited 2 times 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 value of  [#permalink]

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New post 10 Dec 2012, 02:11
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 value of  [#permalink]

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New post 10 Dec 2012, 02:33
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 value of  [#permalink]

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New post 10 Dec 2012, 02:43
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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Re: If ((x + 4)^2)^(1/2) = 3, which of the following could be the value of  [#permalink]

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New post 10 Dec 2012, 04:44
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 value of  [#permalink]

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New post 30 Jan 2018, 11:23
davidfrank 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


Simplifying the left hand side of the equation, we have:

|x + 4| = 3

Thus x + 4 = 3, or x + 4 = -3.

If x + 4 = 3, then x = -1, and so x - 4 = -5.

If x + 4 = -3, then x = -7, and so x - 4 = -11.

Since -5 is not one of the answer choices, the answer must be -11.

Answer: A
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Re: If ((x + 4)^2)^(1/2) = 3, which of the following could be the value of   [#permalink] 30 Jan 2018, 11:23
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