Analysis: Known: 30? =900,3 1? =96 1, so there is: 30 < √ 925 < 3 1, that is, the number obtained by squaring 925 is not an integer, between 30 and 3 1. There is also 925=25×37, where 25=5×5 and 37 is not a square number, so it cannot be squared.
So we can work out: √925=5√37.
Common square number:
1 1^2= 12 1
12^2= 144
13^2= 169
14^2= 196?
15^2=225 ?
16^2=256?
17^2=289?
18^2=324?
19^2=36 1?
20^2=400 ?
Extended data:
Characteristics of complete square numbers:
1, essence: after the prime factor is decomposed, each prime factor is even.
2. Nature: I mean odd cause.
3. In the factorization of a complete square number, the exponent of each prime factor is even, and vice versa.
4. The number of factors of a complete square number is odd, and vice versa.
5. The number of factors of 3 must be the square of prime numbers.
Forward derivation: If you know the unit number of a natural number n, then you also know the unit number of N2.
Backward derivation: Knowing the unit number of N2, we can estimate the unit number of natural number n..