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

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Joined: 21 Jun 2011
Posts: 75
Location: United States
Concentration: Accounting, Finance
WE: Accounting (Accounting)
If ((x + 4)^2)^(1/2) = 3, which of the following could be the value of [#permalink]

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Updated on: 25 Dec 2017, 22:55
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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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Joined: 02 Sep 2009
Posts: 45360
Re: If ((x + 4)^2)^(1/2) = 3, which of the following could be the value of [#permalink]

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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 $$x-4=-11$$.

Hope it's clear.

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Joined: 21 Jun 2011
Posts: 75
Location: United States
Concentration: Accounting, Finance
WE: Accounting (Accounting)
Re: If ((x + 4)^2)^(1/2) = 3, which of the following could be the value of [#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: 45360
Re: If ((x + 4)^2)^(1/2) = 3, which of the following could be the value of [#permalink]

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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 $$x-4=-11$$.

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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Joined: 24 Apr 2012
Posts: 48
Re: If ((x + 4)^2)^(1/2) = 3, which of the following could be the value of [#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 value of [#permalink]

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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.

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

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