第3章平方根和平方根–练习3.1 |套装1
问题9。找出最大的两位数，即一个完美的平方。
解决方案：
Greatest two-digit number is 99
99 = 81+18
= 9×9 + 18
18 is the remainder
Perfect square number is 99 – 18 = 81
Therefore, the greatest number of two digits which is perfect square is 81
问题10。找到最少的三位数，这是一个完美的正方形。
解决方案：
Least three-digit number is 100
100 = 10 × 10
100 itself is the square of 10
Therefore, the least number of three digits which is perfect square is 100
问题11。找出必须乘以4851的最小数，以使乘积成为一个理想的平方。
解决方案：
Prime factorization of 4851
4851 = 3×3×7×7×11
By grouping the prime factors
= (3×3) × (7×7) × 11
11 is left out
Therefore, the smallest number by which 4851 must be multiplied so that the product becomes a perfect square is 11.
问题12。找到必须除以28812的最小数，以使商成为一个完美的平方。
解决方案：
Prime factorization of 28812
28812 = 2×2×3×7×7×7×7
By grouping the prime factors
= (2×2) × 3 × (7×7) × (7×7)
3 is left out
Therefore, the smallest number by which 28812 must be divided so that the quotient becomes a perfect square is 3.
问题13。找出必须除以1152的最小数，以使其成为一个完美的正方形。还要找到其平方为所得数字的数字。
解决方案：
Prime factorization of 1152
1152 = 2×2×2×2×2×2×2×3×3
By grouping the prime factors
= (2×2) × (2×2) × (2×2) × (3×3) × 2
Therefore, the smallest number by which 1152 must be divided so that the quotient becomes a perfect square is 2.
The number after division, 1152/2 = 576
Prime factors for 576 = 2×2×2×2×2×2×3×3
By grouping the prime factors
= (2×2) × (2×2) × (2×2) × (3×3)
= (2×2×2×3) × (2×2×2×3)
= 242
Therefore, the resulting number is square of 24.