第3章平方根和平方根–练习3.2 |套装1
问题11.以下哪个数字是偶数的平方?
121、225、256、324、1296、6561、5476、4489、373758
解决方案：
Only even numbers be the square of even numbers.
So, 256, 324, 1296, 5476, 373758 are even numbers
But 373758 is not a perfect square as unit digit is 8
Therefore, 256, 324, 1296, 5476 are squares of even numbers.
问题12.通过仅检查单位数字，您能否确定以下哪个不是整数?
(i)1026
解决方案：
As unit digit is 6
Therefore,it can be a perfect square.
(ii)1028
解决方案：
As unit digit is 8
Therefore, it can not be a perfect square.
(iii)1024
解决方案：
As unit digit is 4
Therefore, it can be a perfect square.
(iv)1022
解决方案：
As unit digit is 2
Therefore, it can not be a perfect square.
(v)1023
解决方案：
As unit digit is 3
Therefore, it can not be a perfect square.
(vi)1027
解决方案：
As unit digit is 7
Therefore, it can not be a perfect square.
问题13.您无法确定哪个数字是平方数。
解决方案：
We know that the natural numbers ending with digits such as 0, 1, 4, 5, 6 or 9 cannot be decided surely whether they are squares or not.
问题14.写下五个数字，仅通过查看本机的数字就无法确定它们是否为正方形。
解决方案：
We know that any natural number ending with 0, 1, 4, 5, 6 or 9 can be or cannot be a square number.
Here are the five examples which you cannot decide whether they are square or not just by looking at the units place:
(i) 2061
The unit digit is 1. So, it may or may not be a square number
(ii) 1069
The unit digit is 9. So, it may or may not be a square number
(iii) 1234
The unit digit is 4. So, it may or may not be a square number
(iv) 56790
The unit digit is 0. So, it may or may not be a square number
(v) 76555
The unit digit is 5. So, it may or may not be a square number
问题15.对以下陈述，写“真”(T)或“假”(F)。
(i)平方数中的位数是偶数。
解决方案：
False, because 121 is a square number with odd number of digits.
(ii)质数的平方是质数。
解决方案：
False, because the square of 5(which is prime) is 25(which is not prime).
(iii)两个平方数之和是一个平方数。
解决方案：
False, because sum of 12 and 22 is 5 which is not a square number.
(iv)两个平方数之差为平方数。
解决方案：
False, Difference of 42 = 16 and 32 = 9 is 7 which is not a prefect square.
(v)两个平方数的乘积是一个平方数。
解决方案：
True, 32=9, 42=16 Product is 144 which is square of 12.
(vi)没有平方数为负。
解决方案：
True, because (-3)2 is 9, which is not negative.
(vii)50和60之间没有平方数。
解决方案：
True, because as there is no square number between them.
(viii)共有14个平方数，最大为200。
解决方案：
True, because square numbers up to 200 are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196.