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You need to know the base for the modulo arithmetic. If the base is the integer p, then 31 can be expressed as n*p + r, or r is the remainder when 31 is divided by p. r is also called the primitive root of 31 modulo p. The primitive root of 31, by itself, has no meaning. It is only in relation to p that it has a meaning and a value. p = 2: primitive root = 1 p = 3: primitive root = 1 p = 4: primitive root = 3 p = 5: primitive root = 1 p = 7: primitive root = 3 p = 8: primitive root = 7 etc.
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There is no real number [square] root of a negative number. There is a real cube root and a real fiftth root etc, but root, by itself, implies square root.
The square root is the number which is times by itself, to get the square number.
the square root of a number is the number that is multiplied by itself to get that number, for example the square root of 9 is 3