Please explain

[navdeep_bajwa]

I read that in Official GMAT 12th edition (x^2)^1/2 denotes the non negative square root of x^2, and so (x^2)^1/2=abs x

Can anyone please explain this if x=3 then x^2=9 and root of x has two values -3 and 3 then how can be root of x abs 3 and not +3 and -3

Also x^1/2 denotes the positive number whose square is x again the same question why cannot x has both + and - values

[rp.gill2]

Cause you apply BODMAS rule (or several similar variants) you first solve brackets, then power (signified by O or Off...) then anything else.

Now (X^2)^1/2 should be solved as 1/2 canceling 2 leaving X. Not the square first and then square root.

Hope that helps

[navdeep_bajwa]

I donot get it

(x^2)^1/2=abs x

if x=-5 then (x^2)^1/2=+-5 and if we cancel 2 by 1/2 it then leaves -5 but not abs 5

[Ben Ku]

Now (X^2)^1/2 should be solved as 1/2 canceling 2 leaving X. Not the square first and then square root.

This is incorrect. When you simplify (x^2)^1/2, you first square and then take the square root. Here the order matters.

The question is, why is (x^2)^1/2 = | x |? Basically, when you square a number, it becomes positive; taking the square root will keep it positive. So after taking the square and then the square root of x, you get only the positive value of x.

So if x = -5, then (x^2)^1/2 = ((-5)^2)^1/2 = (25)^1/2 = 5. Now the value of x could be positive or negative, but the value of (x^2)^1/2 is always positive.

The only time when you have to worry about taking the positive and negative answer is when you take the square roots of both sides of an equation. For example,

(x + 3)^2 = 25
Then x + 3 = 5 or x + 3 = -5

Hope that helps.