Question

Make the list of all perfect squares from $ 1 $ to $ 500 $

Answer 1

Hint: We will start listing the squares of each number starting from $ 1 $ till we get a number greater than $ 500 $ . After doing this we will list all the squares of numbers less than $ 500 $ and that will be our required answer. We will then enlist the numbers one by one.

Complete step-by-step answer:
Let’s make a table to list the squares:

$ a $	$ {a^2} $
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100
11	121
12	144
13	169
14	196
15	225
16	256
17	287
18	324
19	361
20	400
21	441
22	484
23	529

Clearly, we have all the values of $ {a^2} $ till $ a = 23 $ , and we found that the squares after $ a = 23 $ will generate a value greater than $ 500 $ . But according to the question we have to list all the perfect squares from $ 1 $ to $ 500 $ .
Therefore we will list all the squares of numbers from $ 1 $ to $ 23 $ .
The list of all perfect squares from $ 1 $ to $ 500 $ is
1,4,9,16,25,36,49,56,81,100,121,144,169,196,225,256,287,324,361,40,441,484,529
So, the correct answer is“1,4,9,16,25,36,49,56,81,100,121,144,169,196,225,256,287,324,361,40,441,484,529”.

Note: While calculating the square always use a neat paper to do the calculation because it takes a lot of effort and hard work, clean paper helps in focusing calculations better than any paper that is not a clean one. Also while listing the numbers always crosscheck if you missed any numbers, because very often while doing a lot of calculations some numbers get missed without our knowledge.