Introduction
In mathematics, a Square of a Number or Perfect square is an integer that is the square of an integer; in other words, it is the product of an integer with itself.
The usual notation for the square of a number n is not the product n × n, but the equivalent exponentiation [latex]n^2[/latex]
[latex]n^2 = n × n[/latex]
Tips
How to quickly Calculate the Square of a 2-digit number in 10 seconds?
If you have to find the square of any number then you have to follow these steps for a 2 digit number of the form AB.
Step 1: Apply this formula : [latex]A^2 . 2 * A * B . B^2[/latex]
Step 2: Calculate from Right to Left. Take the 1st digit and carry the 2nd digit and add carry to the next value and take the 1st digit and carry the 2nd digit and add the carry to the next value and take the total sum.
Examples: 1. [latex]36^2[/latex] = ?
2. [latex]42^2[/latex] = ?
Shortcuts
Case 1: Square of any number ending in 5. i.e. unit digit is 5 (example. 35).
Logic: Let us take a two digit number n5 whose unit digit is 5.
Square of n5 i.e. [latex](n5)^2[/latex] = n(n+1)/25
Example: 35
[latex]35^2[/latex] = 3(3+1)/25
= 3(4)/25
= 1225.
Table
| Number | Square | Value |
|---|---|---|
| 1 | [latex]1^2[/latex] | 1 |
| 2 | [latex]2^2[/latex] | 4 |
| 3 | [latex]3^2[/latex] | 9 |
| 4 | [latex]4^2[/latex] | 16 |
| 5 | [latex]5^2[/latex] | 25 |
| 6 | [latex]6^2[/latex] | 36 |
| 7 | [latex]7^2[/latex] | 49 |
| 8 | [latex]8^2[/latex] | 64 |
| 9 | [latex]9^2[/latex] | 81 |
| 10 | [latex]10^2[/latex] | 100 |
| 11 | [latex]11^2[/latex] | 121 |
| 12 | [latex]12^2[/latex] | 144 |
| 13 | [latex]13^2[/latex] | 169 |
| 14 | [latex]14^2[/latex] | 196 |
| 15 | [latex]15^2[/latex] | 225 |
| 16 | [latex]16^2[/latex] | 256 |
| 17 | [latex]17^2[/latex] | 289 |
| 18 | [latex]18^2[/latex] | 324 |
| 19 | [latex]19^2[/latex] | 361 |
| 20 | [latex]20^2[/latex] | 400 |
| 21 | [latex]21^2[/latex] | 441 |
| 22 | [latex]22^2[/latex] | 484 |
| 23 | [latex]23^2[/latex] | 529 |
| 24 | [latex]24^2[/latex] | 576 |
| 25 | [latex]25^2[/latex] | 625 |
| 26 | [latex]26^2[/latex] | 676 |
| 27 | [latex]27^2[/latex] | 729 |
| 28 | [latex]28^2[/latex] | 784 |
| 29 | [latex]29^2[/latex] | 841 |
| 30 | [latex]30^2[/latex] | 900 |
| 31 | [latex]31^2[/latex] | 961 |
| 32 | [latex]32^2[/latex] | 1024 |
| 33 | [latex]33^2[/latex] | 1089 |
| 34 | [latex]34^2[/latex] | 1156 |
| 35 | [latex]35^2[/latex] | 1225 |
| 36 | [latex]36^2[/latex] | 1296 |
| 37 | [latex]37^2[/latex] | 1369 |
| 38 | [latex]38^2[/latex] | 1444 |
| 39 | [latex]39^2[/latex] | 1521 |
| 40 | [latex]40^2[/latex] | 1600 |
| 41 | [latex]41^2[/latex] | 1681 |
| 42 | [latex]42^2[/latex] | 1764 |
| 43 | [latex]43^2[/latex] | 1849 |
| 44 | [latex]44^2[/latex] | 1936 |
| 45 | [latex]45^2[/latex] | 2025 |
| 46 | [latex]46^2[/latex] | 2116 |
| 47 | [latex]47^2[/latex] | 2209 |
| 48 | [latex]48^2[/latex] | 2304 |
| 49 | [latex]49^2[/latex] | 2401 |
| 50 | [latex]50^2[/latex] | 2500 |
| 51 | [latex]51^2[/latex] | 2601 |
| 52 | [latex]52^2[/latex] | 2704 |
| 53 | [latex]53^2[/latex] | 2809 |
| 54 | [latex]54^2[/latex] | 2916 |
| 55 | [latex]55^2[/latex] | 3025 |
| 56 | [latex]56^2[/latex] | 3136 |
| 57 | [latex]57^2[/latex] | 3249 |
| 58 | [latex]58^2[/latex] | 3364 |
| 59 | [latex]59^2[/latex] | 3481 |
| 60 | [latex]60^2[/latex] | 3600 |
| 61 | [latex]61^2[/latex] | 3721 |
| 62 | [latex]62^2[/latex] | 3844 |
| 63 | [latex]63^2[/latex] | 3969 |
| 64 | [latex]64^2[/latex] | 4096 |
| 65 | [latex]65^2[/latex] | 4225 |
| 66 | [latex]66^2[/latex] | 4356 |
| 67 | [latex]67^2[/latex] | 4489 |
| 68 | [latex]68^2[/latex] | 4624 |
| 69 | [latex]69^2[/latex] | 4761 |
| 70 | [latex]70^2[/latex] | 4900 |
| 71 | [latex]71^2[/latex] | 5041 |
| 72 | [latex]72^2[/latex] | 5184 |
| 73 | [latex]73^2[/latex] | 5329 |
| 74 | [latex]74^2[/latex] | 5476 |
| 75 | [latex]75^2[/latex] | 5625 |
| 76 | [latex]76^2[/latex] | 5776 |
| 77 | [latex]77^2[/latex] | 5929 |
| 78 | [latex]78^2[/latex] | 6084 |
| 79 | [latex]79^2[/latex] | 6241 |
| 80 | [latex]80^2[/latex] | 6400 |
| 81 | [latex]81^2[/latex] | 6561 |
| 82 | [latex]82^2[/latex] | 6724 |
| 83 | [latex]83^2[/latex] | 6889 |
| 84 | [latex]84^2[/latex] | 7056 |
| 85 | [latex]85^2[/latex] | 7225 |
| 86 | [latex]86^2[/latex] | 7396 |
| 87 | [latex]87^2[/latex] | 7569 |
| 88 | [latex]88^2[/latex] | 7744 |
| 89 | [latex]89^2[/latex] | 7921 |
| 90 | [latex]90^2[/latex] | 8100 |
| 91 | [latex]91^2[/latex] | 8281 |
| 92 | [latex]92^2[/latex] | 8464 |
| 93 | [latex]93^2[/latex] | 8649 |
| 94 | [latex]94^2[/latex] | 8836 |
| 95 | [latex]95^2[/latex] | 9025 |
| 96 | [latex]96^2[/latex] | 9216 |
| 97 | [latex]97^2[/latex] | 9409 |
| 98 | [latex]98^2[/latex] | 9604 |
| 99 | [latex]99^2[/latex] | 9801 |
| 100 | [latex]100^2[/latex] | 10000 |