Multiplying 2 is a complete square number, so the powers of 3 and 5 must be multiples of 2, and the power of 2 is odd.
Multiplying 3 is a complete cubic number, then the powers of 2 and 5 must be multiples of 3, and the power of 3 is multiples of 3 minus 1.
Multiplying by 5 is a complete fifth power, then the powers of 2 and 3 must be multiples of 5, and the power of 5 is multiples of 5 minus 1.
All in all,
The power of 2 is a multiple of 3 and 5, and it is odd, and the minimum value is 15.
The power of 3 is a multiple of 2 and 5, a multiple of 3 minus 1, and the minimum is 20.
The power of 5 is a multiple of 2 and 3, a multiple of 5 minus 1, and the minimum is 24.
So the smallest natural number is:
15 squared * 20 squared * 24 squared.
2、 125
3. Test center: the nature of the complete square number. Analysis: 72 = 23× 32. As long as the multiplied number is twice the square number and the product is a complete square number, we can solve it. Solution: Because 72 = 23× 32. As long as the multiplied number is twice the square number, the product is a complete square number. 1998 ÷ 2.
Answer: There are 3 1 number multiplied by 72, which is a complete square. Comments: This question examines the nature and analytical reasoning ability of students' complete square.