What is the value of p?

Source: Self-made
Hi Bunuel, chetan2u, MathRevolution, GMATinsight, EMPOWERgmatRichC,
I'm totally stuck with my own solution . Can you help me with your expert solution?
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.
(2) 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?

I’m totally stuck with this question; I can’t make decision which one will be correct answer among B, D, and E.

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.
Thank you all GMAT club members.