What is the value of p

[MdAbuAsad]

What is the value of p?
(1) p^2=100
(2) p=√100

Source: Self-made
Hi Ron,
I'm stuck with my own creative problem-I can’t make decision which one will be correct answer among B, D, and E. Can you help me to find the correct answer?
Here is the Solution:
Approach-1,

Statement 1:
p^2=100
---> if p=10, then 10^2=100
---> again, if p= -10, then (-10)^2=100, too.
--->So, p=10 or -10.
---> Not Sufficient.
Statement 2:
p=√100
---> p=10 only…. (not -10)
--->Sufficient.
---> So, the correct answer is B, right?

Approach-2,
If I start from Statement 1, then I’ll get the following equation.
p^2=100
---> √(p)^2=√100 [making root in both side]
---> p=√100
---> which is IDENTICAL to statement 2
---> Here, p gives just 1 value to legitimate THIS equation.
---> So, here the value of p=10.
---> Sufficient…
---> So, the correct answer is D, right?

Approach-3,
If I make the creativity in statement 2, I’ll get the following equation.
p=√100
---> (p)^2=(√100)^2
---> p^2=100
---> which is IDENTICAL to statement 1.
So, I’m again in my last line of equation, which is given below.
--->p^2=100
---> Here, p gives 2 values to legitimate THIS equation.
--->P may be 10, or p may be -10.
---> Insufficient…
So, the correct answer is E, right?

N.B.: If the statement 1 and 2 are identical to each other, then there is a chance to be the answer ONLY either D or E.
If any of the statements sufficient, then it is pretty sure that BOTH statements are sufficient independently/simultaneously because they are identical to each other. If this happen, the correct answer will be D.
Again, if any of the statements are NOT sufficient, then it is going to be answer E because they are identical to each other.

[RonPurewal]

your "approach 1" is correct. the "√" symbol -- like every other mathematical symbol -- means exactly one thing.

i don't understand what you are doing in the other two approaches, but whatever you're doing in those approaches is incorrect.

[MdAbuAsad]

I'm going to make identical each statement.
Here is the statement 1:
p^2=100
---> √(p)^2=√100 [making root in both side]
---> (p^2)^(1/2)=√100
---> p^(2/2)=√100
---> p=√100, which is statement 1.
Ron, is there any mistake in my calculation?
Thank you...

[RonPurewal]

the first step doesn't work, because the "√" symbol represents a positive number.

like if n^2 = 7, for instance, then n could be either √7 or –√7. so, the next step in that case would be n = ±√7.

[RonPurewal]

if you are paying any thought at all to what these symbols mean, then, you should be able to critique your own steps here.
it should be clear enough that there are two different numbers that you can square to get 100: namely, 10 and –10.
therefore, any approach that gives only one value for p^2 = 100 is clearly wrong, and you should reject it automatically.

(if you legitimately can't see the problem here, then, you are basically just shifting meaningless symbols around a page according to completely arbitrary rules. that is ... not a headspace where you want to be.)