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

Question

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 nonnegative
E. None of the above

PareshGmat · Accepted Answer

We require to find what must be true rather than what can be true?

Testing all options:

a) x is positive >> Not necessary >>  \sqrt{0} = 0

b) x=1 >> Not necessary >> x can be zero  \sqrt{0} = 0

c) square(x)>x >> Not necessary >> For x=1 or x = 0,  x^2 = x

d) x is nonnegative >> That's correct >> x has to be non-negative because square root of a negative integer cannot be the same integer

\sqrt{-1}
eq{1}

e) none of the above >> D hold true

Answer = D

manpreetsingh86 · Answer

√x=x; squaring both sides we have
x=x^2
x(x-1)=0
x=0 or 1

lets look in to the each option

a) x can be zero as well, which is neutral (neither positive nor negative) hence out
b) x can be zero as well
c) clearly out
d) this must be true. as non negative, satisfies both x=0 and x=1

hence D

EMPOWERgmatRichC · Answer

Hi All,

This question is really more about the 'thoroughness' of your thinking than anything else. Most Test Takers would look at this question and think "Oh, the answer is obviously X=1....", but is that really the ONLY answer???

The numbers -1, 0 and 1 have all sorts of interesting 'impacts' on how various math rules 'work', so it's important to keep them in mind as you work through the Quant section of the GMAT.

Here, we're asked what MUST be true based on the equation √x = x. You should be able to determine the 2 solutions to this equation (whether you do the formal algebra or not). Those solutions are 0 and 1. Using those answers as reference, only one of the 5 answers choices is correct...

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

jfranciscocuencag · Answer

\sqrt{x}=x

\sqrt{x}^2=x^2

x = x^2

0 = \frac{x^2}{x}

0 =x

Nonnegative

D

gagan543 · Answer

Thank you for the explanation,but i still have a question how is statement "A" and statement "D" differ in term of the meaning.
like statement "D" says x is a non negative number ,is it not same as "A" which says that x is a positive

Bunuel · Answer

A. x is positive means  x > 0

D. x is nonnegative means  x \geq 0

As you can see option D allows x to be 0 too.

MHIKER · Answer

An important Property is:  The square root of something can't be negative

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

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

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