# Is √x² = x or -x or none.

Crawl through various forums of mathematics & MBA preparation and you will find people searching for a clue whether √x² = x or -x or what ….

**Quotlly**

Now to solve this situation, always remember in mind. √X is always a positive number where X is a real number

say for e.g. √25 = 5 a +ve number. √(-5)2 = 5 or √(5)2 = 5.

√36 = 6 a +ve number.

similarly √x² is always a +ve number.

**So why can’t we write √x² = x ????? –> NO**

Think before you write. Do you know that x is positive or negative. NO. but you know that √x² is a positive number.

positive number =/= negative number.

For e.g. x=-5 , so √(-5)² =/= -5

but √(-5)² = 5 = -(-5) =-x

**So can we write √x² = -x ????? —> NO **

Again think. what will happen if x is a positive number.

For e.g. x=5 , so √(5)² =/= -5

but if x=5, √(5)² = 5 =x.

**So what is this √x² basically.**

Going through the above examples again we find that, the magnitude of the final result is same but there is a difference in sign (+ or -) depending on the value of x.

so to make **√x² compatible with RHS, **we will have to make RHS always +ve.

So **√x² = |x| , **which is always true.

where **|x|** is** absolute value or modulus **of x

and √x² = |x| = x if x >0 and -x if x<0.

*If you feel more points could/should be added. Please add in comments , we would edit the post as required.*