exam Maths Puzzle Numerical Ability

for how many integral values of M is m2(m square) 100m + 1000is a perfect squre

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Please help with this problem.
Z=sqrt((1000^2)+(1592^2))
It is my understanding that the square root of a "number" squared is the "number".
If this is true I would solve this as: Z=1000+1592 so Z=2592, but Im not sure this is correct Compare equation with one variable to equations with two variables.

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