Problem Solving

If X<0, The sq root of (-XlXl) is what?

Was a bit confused when i saw this one, I though the sq root of a negative no. is not rational. Can some one help with the fundamentals on this one?

Thanks a lot

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If X<0, -X = -(-X) = X

and |X| = X

So sqrt(-X|X|) = X

Hey Thanks for the reply. I used a similar logic and gave the same ans, but was wrong. The answer is -X.

Have no idea why plus am still puzzled by the basic fundamentals.

take x=-2

The sq root of (-(-2)l-2l) = 2
this value is -(-2) = -(-x)

Only other thing I can think of is

sqrt(X^2) = X and -X

What are the options?

Here is a print screen of the actual test, my answer was X but I was wrong. Answer is -X.

I have no idea how they come up with that answer.

Now that I know the answer, here is my explanation.

By definition,
|x| = x if x>0
-x if x<0


since x<0

sqrt( -x |x|) = sqrt( -x -x) = -x

but, I would have probably not thought of this before.

I think this qs is some thing very tricky because the answer can be x as well as -x. Without knowing the answer before, we all may chose the answer - x. But now tell me how do u know that test-taker is looking for -x as x < 0. Because sqrt(-x|x|) = x or -x even if x < 0. God knows how to face this type of qs!

People we have had quite a lot of discussion on a similar problem some time back....

there is one very important thing to remember regarding square roots the Square root of a number is always positive

for eg. sqroot of 4 is 2... not 2 and -2 , 2 and -2 are the roots of the equation x^2-4=0, which simply means that 2 and -2 will both fulfill the above equation, but when we are talking about sqroot of a number it is always considered to be the positive root..

In the above question we have to find the sqroot(-Xmod(X)) where X<0 ...

Let X = -2, so we have to find the sqroot of (-(-2)mod(-2)) which is basically (2*2), so the square root is 2 .. but X = -2 therefore 2 = -X .. hence the answer is -X ...

Hope that helps ..

Thanks gabriel.... good one

Yop Gabriel! Now got it. Thanks a lot, sir!!! So in such type of problem we have to do a kind of back-track...

anytime guys !!

gabriel, (thanks for sending me this link...)

Absolute value should be always positive...no?


your example is this (-(-2)mod(-2)) but I wonder it should be (-(-2)mod(2)) ??

magical cook wrote:gabriel, (thanks for sending me this link...)

Absolute value should be always positive...no?


your example is this (-(-2)mod(-2)) but I wonder it should be (-(-2)mod(2)) ??

I think ur getting confused about what exactly is modulus of a number ..

Let me just give a few examples

Mod(-2) = 2 and Mod(2)= 2 .. so what that means the mod of both -2 and 2 is the same ... 2 ..

in the question it says x is < 0 .. thats why the example of -2 ...

Does that help .. or am i misreading your query ?

Ok - I think I got it . Thank you for explanation