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

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

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10 Dec 2012, 01:58
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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, 02:07, 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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10 Dec 2012, 02:11
Expert's post
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 $$x-4=-11$$.

Hope it's clear.

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

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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 $$x-4=-11$$.

Hope it's clear.

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.
Math Expert
Joined: 02 Sep 2009
Posts: 32564
Followers: 5642

Kudos [?]: 68466 [0], given: 9805

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

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10 Dec 2012, 02:43
Expert's post
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 $$x-4=-11$$.

Hope it's clear.

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 [#permalink]

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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 [#permalink]

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15 Oct 2014, 16:34
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Re: If ((x+4)^2)^1/2=3, which of the following could be the   [#permalink] 15 Oct 2014, 16:34
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