Inequalities

Its simply [-X]

to visulalize yourself pls take x=-5 and proceed.

hey shantanu

Could u mathematically solve the expression.

Thanks

If I understand the ques correctly, we need to find sq. root of -X times |X|.

I think the answer would be X.

If X<0, -X would be a positive term. -X times |X| = X^2. Hence the sq. root would be X.

yes u did understand the ques correctly. i also found the same answer but OA is -X.... hw? don't know

Hi Abhinav,

This is an important concept. And when one first comes around it, it seems a little difficult to digest.

Let's try to understand this.

First of all: By definition the square root of any Quantity is a positive number. Always!

If x > 0,
x^2 > 0.
square root(x^2) = x (a positive number)

But if x < 0,
x^2 > 0
While taking the square root of x^2 now we have to keep in mind that square root(x^2) should be a positive number.
So, if square root(x^2) = x, then it's negative because x is negative.
To respect the definition of square root, a '-1' is multiplied to x to retain the value but change the sign.

now,
square root(x^2) = -x (which is a positive number. Isn't it?)

Thus
square root(x^2) = x when x > 0
square root(x^2) = -x when x < 0.

If you notice, this is same as the definition of modulus, which states that
|x| = x when x > 0
|x| = -x when x < 0.

To put the definition of square root(x^2) concisely

square root(x^2) = |x|