If the square root of x is x, then what value must x have?
The definition of a square root of x is a number y such that y^2 = x. Clearly,in this case x^2 = x. So x cannot be a negative number because x^2 must be positive or zero. It is clear also that both 0 and 1 are solutions, since 0 times 0 = 0 and 1 times 1 = 1. It is clear also that no other value will work since, if the value of x is not zero, then we may divide both sides of the equation x^2 = x by x to get the result x = 1.
More Info:
en.wikipedia.org
What are your thoughts on this subject?
60 Comments
Chip Amos
Huge problem....the word "value" is used. "0" has no value.
26
Feb 21, 2017 11:55PM
drkegrossman
0 is not a number! Their question is BS!
24
Feb 21, 2017 7:18PM
Ray Brylski
Since zero is neither positive nor negative, its square root is undefined.
21
Feb 21, 2017 11:43PM
Jim Laughner
I knew there would be dispute here from people who do not understand basic arithmetic.
What is 0X0=?
What is 1X1=?
It can't get any more simple than that.
Zero squared is zero, therefore the square root of zero is zero.
One squared is one, therefore the square root of one is one.
I would say "Problem solved, but there is no problem to solve.
Keep things simple and your life will be simplified, throw in altered definitions and other non-existent variables and you can complicate even the simplest of things.
14
Feb 23, 2017 6:37PM
Steve Edwards
I despair at all those who consider that 0 isn’t a number.
It’s true that 0 was, at first, a placeholder (about 1000 years ago), but its usefulness as a number in its own right was quickly realised. It’s a nonsense to suggest that our “number line” has a gap in it where zero is because zero isn’t a number. Similarly zero IS a value. In the equation x+7=7, solution is x=0, which means that the value of x that makes the equation true is zero.
8
Sep 19, 2020 3:42AM
Jim Laughner
Ray Brylski, Zero is defined as "nothing" or "None".
The number 0 fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems.
If you multiply nothing by nothing you have nothing, therefore nothing squared, (or nothing times itself), is still nothing. From that, it stands to reason that the square root of nothing is nothing. Call it what you want but when you multiply it by itself or divide it by itself the answer is the same, NOTHING or ZERO, or ZERO, or ZILCH, or any other of other terms commonly used.
5
Feb 23, 2017 6:50PM
Phil Kennelty
0 times 0 does not equal 0.
4
Jun 29, 2023 12:39PM
Mary Elizabeth Mazi Ross
drkegrossman, I agree
1
Apr 3, 2023 3:15PM
Char
drkegrossman, exactly this isn't a math quiz anyway.Always putting others down for thier questions better than his to me
0
Mar 29, 2023 11:58PM
james parrillo
Jas Newman, Why? Thank you for explaining further. Christine, James' wife
1
Mar 29, 2023 11:41PM
Jas Newman
Peter Abrams, True. but that wasn't the question. In the case of the question, X cannot be -1.
1
Mar 28, 2023 7:03PM
Howard Groopman
I thought zero was not considered a number, and that anything divided by zero is infinity.
2
Mar 12, 2023 8:28PM
Glynis Rix
No clue what's happening!
0
Mar 8, 2023 1:14AM
Peter Abrams
Jim Laughner, yes the square root of 1 is 1, but it’s also -1.
0
Mar 4, 2023 5:29PM
earlepg
Al Breyette, I've already said the same thing. Except, as is true this time, I rarely notice the authors name until after I've already answered the question. I luckily anwered this question right.
0
Mar 4, 2023 8:07AM
Ron Gosling
0 not a number so wrong. Only one is answer.
4
Feb 28, 2023 6:29PM
Peter Abrams
reydlt, if 0 x A=0 then A can be 0. 0x0=0. Therefore the square root of 0 is 0. Division by 0 is undefined, yes. But 0x0 is 0. The square of 0 is not undefined.
0
Feb 17, 2023 10:29PM
reydlt
The square root of 0 is not 0. It is undefined.
4
Feb 10, 2023 3:49AM
Jerry Edwards
drkegrossman,
The question does not mention "number". It asks what value.
1
Jan 31, 2023 5:02AM
Al Breyette
Typical Frank Cowell question. I'm going to start replacing his questions because they are always trick questions or have dubious answers.
2
Jan 18, 2023 8:16AM
Pete Caffall
Division by zero is undefined. Similarly, √0 is undefined .
2
Jan 9, 2023 6:57PM
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