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If √x = x, then which of the following must be true?

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emmak
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If √x = x, then which of the following must be true? [#permalink] New post   Updated on: 22 Mar 2013, 02:54
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If \(\sqrt{x}\) = x, then which of the following must be true?

A. x is positive
B. x=1
C. x^2>x
D. x is non-negative
E. None of the above
ShowHide Answer
Official Answer
D

Originally posted by emmak on 22 Mar 2013, 00:56.
Last edited by Bunuel on 22 Mar 2013, 02:54, edited 1 time in total.
Renamed the topic and edited the question.
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If x = x, then which of the following must be true? [#permalink] New post   Updated on: 14 May 2023, 02:34
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Given that \(\sqrt{x}\)=x and we need to find which of the following must be true?

\(\sqrt{x}\)=x

Squaring both the sides we get:
x = \(x^2\)
\(x^2\) - x= 0
x(x-1)=0
=> x=0 or x=1

So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Roots


Originally posted by BrushMyQuant on 22 Mar 2013, 01:34.
Last edited by BrushMyQuant on 14 May 2023, 02:34, edited 1 time in total.
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Bunuel
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Re: If √x = x, then which of the following must be true? [#permalink] New post   22 Mar 2013, 03:03
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If \(\sqrt{x}= x\) , then which of the following must be true?

A. x is positive
B. x=1
C. x^2>x
D. x is non-negative
E. None of the above

We have that x is equal to the square root of some number (\(\sqrt{x}\)). Now, we know that the square root function cannot give negative result (\(\sqrt{{some \ expression}}\geq{0}\)), thus LHS (\(\sqrt{x}\)) is more than or equal to zero, which implies tha RHS (x) is also more than or equal to zero. Hence we have that \(x\geq{0}\).

Answer: D.

Or simply be solving: \(\sqrt{x}= x\) --> \(x=x^2\) --> \(x(x-1)=0\) --> \(x=0\) or \(x=1\).

Answer: D.
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Re: If √x = x, then which of the following must be true? [#permalink] New post   17 Feb 2018, 03:39
Square it on both sides
x^2=x
x^2-x=0
x(x-1)=0
x=0,1
So D should be the answer because this is a "must be true" question
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Re: If √x = x, then which of the following must be true? [#permalink] New post   19 Jun 2020, 04:10
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only the numbers ''0'' and ''1'' satisfy this expression. Both these numbers are non-negative. Hence, (D) is the right answer choice.
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If √x = x, then which of the following must be true? [#permalink] New post   22 Nov 2020, 06:46
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emmak wrote:
If \(\sqrt{x}\) = x, then which of the following must be true?

A. x is positive
B. x=1
C. x^2>x
D. x is non-negative
E. None of the above



The square root of something can't be negative. \(x\) mus be \(\ge 0\)

The answer is D.

Or,
\(\sqrt{x}^2\) = \(x^2\) Squaring both sides

\(x\) = \(x^2\)

\(x^2-x=0\)

\(x(x-1)=0\)

\(x=0\)

\(x-1=0\), \(x=1\)

So, \(x\) is non-negative.

The answer is D.
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Re: If √x = x, then which of the following must be true? [#permalink] New post   22 Nov 2020, 09:50
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Squaring on both LHS and RHS we get;
x=x2=> x2-x = 0
=>x(x-1) =0
=>x=0 or x=1
Eliminate (a) because for x=0 (because 0 is neither positive nor negative).
Eliminate (b) because x=1 is a possibility and not a “must be “answer.
Eliminate (d) because at x=1, √x= x
Choice (c) is the solution

Hope this helps. Keep working !
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Re: If √x = x, then which of the following must be true? [#permalink] New post   22 Nov 2020, 10:42
emmak wrote:
If \(\sqrt{x}\) = x, then which of the following must be true?

A. x is positive
B. x=1
C. x^2>x
D. x is non-negative
E. None of the above

\(\sqrt{x}= x\) Only when x = 1

Now , check carefully...

\(\sqrt{1}= +1 \) or \(-1\)

Among the given options check if \(x = -1\)

\(\sqrt{-1} = i \) (Imaginary number), So , Only (D) is possible, Answer must be (D)
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Re: If √x = x, then which of the following must be true? [#permalink] New post   23 Nov 2020, 11:06
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CrackVerbalGMAT wrote:
Squaring on both LHS and RHS we get;
x=x2=> x2-x = 0
=>x(x-1) =0
=>x=0 or x=1
Eliminate (a) because for x=0 (because 0 is neither positive nor negative).
Eliminate (b) because x=1 is a possibility and not a “must be “answer.
Eliminate (d) because at x=1, √x= x
Choice (c) is the solution

Hope this helps. Keep working !



Can you please Examplify how does \(x^2>x\) and why D does not answer?
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If √x = x, then which of the following must be true? [#permalink] New post   02 Dec 2020, 03:38
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Hi! MHIKER
Happy to resolve your query. :)
(C) is NOT the choice because the question asks for MUST BE True answer option. At x=1 they are equal and hence (C) is not valid.
(D) is NOT the choice of answer because "0" is neither negative nor positive.
Thank You.Hope this helps :thumbsup:
Devmitra
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Re: If √x = x, then which of the following must be true? [#permalink] New post   02 Dec 2020, 05:52
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Squaring both the sides will give us x = \(x^2\)

=> \(x^2 - x = 0\)

=> x ( x - 1) = 0

=> x = 0 or 1

Answer D
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Re: If x = x, then which of the following must be true? [#permalink] New post   14 May 2023, 00:24
emmak wrote:
If \(\sqrt{x}\) = x, then which of the following must be true?

A. x is positive
B. x=1
C. x^2>x
D. x is non-negative
E. None of the above


gmatophobia BrushMyQuant Bunuel

I picked B based on my understanding of the concept that square roots are always positive. Is this not the case?
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Re: If x = x, then which of the following must be true? [#permalink] New post   14 May 2023, 01:23
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achloes wrote:
emmak wrote:
If \(\sqrt{x}\) = x, then which of the following must be true?

A. x is positive
B. x=1
C. x^2>x
D. x is non-negative
E. None of the above


gmatophobia BrushMyQuant Bunuel

I picked B based on my understanding of the concept that square roots are always positive. Is this not the case?


The square root of a non-negative number is non-negative: \(\sqrt{nonnegative} \geq 0\).
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Re: If x = x, then which of the following must be true? [#permalink] New post   14 May 2023, 02:36
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achloes : Square root of a non-negative number will be non-negative => ≥ 0, that means it can be zero too.

I have also highlighted some concepts of roots in the below video, hope you find it useful.
Thank you.

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Re: If x = x, then which of the following must be true? [#permalink]
14 May 2023, 02:36
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