Confusion when root of a number is to be taken!

Assuming the question is Is x > 12?

Then statement 1

x^1/2 > 4
√x > 4
|x| > 16 (squaring both sides)
|x| > 16 or -16

Does not make sense. Not sufficient

Statement 2

x > 144^1/2

x > √144

x > 12 Sufficient

What is the source? And the question appears odd!

when you say √x > 4, on squaring √x, we are always going to get a +ve number right? so shouldn't we directly assume x > 16?

I am confused over the way you have used second statement.
statement : x > √144
can't we say here that x > 12 or x > -12, if we have the second case, we can't be sure that x >12?
Also my question is whether taking -ve root acceptable here? if not, why so?

apurva.jalit wrote:when you say √x > 4, on squaring √x, we are always going to get a +ve number right? so shouldn't we directly assume x > 16?

I am confused over the way you have used second statement.
statement : x > √144
can't we say here that x > 12 or x > -12, if we have the second case, we can't be sure that x >12?
Also my question is whether taking -ve root acceptable here? if not, why so?

Hi,

There are 2 different scenarios

See square of a number, say -4 or 4 is always 16, but √ of a number is usually taken as positive, such as √16 is 4.

Both the cases we need to find the value of x, so in statement 1 we don't have a direct equation mentioning the value of x, so we have to find a solution for x, so it is like this √x is nothing but x ^1/2 so squaring results in (x^1/2)^2, so we get x.

Also we cannot square root a negative number.It is convention that is followed, symbols need to have 1 value.

So for your query:

1. No you cannot assume that a solution for a square of a number is always positive, it can be negative or positive. You have to find the solution.

2. Square root of a number(Usually symbols have one value only) has to be positive, that's a convention followed to remove ambiguity.