# [Maths Class Notes] on Square Numbers Pdf for Exam

According to the square number definition, they are the numbers that are multiplied by themselves. In other words, if a natural number is multiplied by itself, it is known as a square number. For example, 2 multiplied by itself (2×2) is a square number. When we multiply two equal integers by each other, the result of that ticket is basically a perfect square. Square numbers cannot be negative because if a negative number is multiplied by the same negative number it results in a positive number. Hence, square numbers are always positive.

Square numbers are named after a square because they form an area of a square. Imagine you have 9 items of 3 different categories. If we arrange it into a grid of 3 columns and 3 rows (3*3=9) placed vertically and horizontally, the grid will form a square.

### Squaring Decimals

Just like squaring whole numbers (integers) is easy, it is also very easy to square decimals and both are done in the same way.

For example, 1.53 x 1.53 = 2.3409

7.19 x 7.19 = 51.6961

### Properties of Square Number

• Property 1- Square numbers will always end with the digits 0,1,4,5,6 and 9. For example 9,14,25,81,100 are perfect squares whereas numbers like 17,22,83 are not perfect numbers.

• Property 2- A square number always contains an even number of zeros at the end and numbers containing an odd number of zeros cannot be square numbers. For example, 1600 3600  2500 square numbers whereas 1000, 250,160 are not square numbers.

• Property 7- Square root of a square number is a whole number. For example, the square root of 441 is 21 so your 441 is a square number. If the square of a number is a decimal of a fraction number then the number is not a perfect square. For example, √56=7.48, so your 56 is not a perfect square.

1²=1

2²=1+3

3²=1+3+5

4²=1+3+5+7 and so on.

(2m,m²-1,m²+1) is a Pythagorean triplet.

Below  is the Table of Square Numbers From 1 to 100:

 1²=1 21²=441 41²=1691 61²=3721 81²=6561 2²=4 22²=484 42²=1764 62²=3844 82²=6724 3²=9 23²=529 43²=1849 63²=3969 83³=6889 4²=16 24²=576 44²=1936 64²=4096 84²=7056 5²=25 25²=625 45²=2025 65²=4225 85²=7225 6²=36 26²=676 46²=2116 66²=4356 86²=7396 7²=49 27²=729 47²=2209 67²=4489 87²=7569 8²=64 28²=784 48²=2304 68²=4624 88²=7744 9²=81 29²=841 49²=2401 69²=4721 89²=7921 10²=100 30²=900 50²=2500 70²=4900 90²=8100 11²=121 31²=961 51²=2601 71²=5041 91²=8281 12²=144 32²=1024 52²=2704 72²=5184 92²=8464 13²=169 33²=1089 53²=2809 73²=5329 93²=8649 14²=196 34²=1156 54²=2916 74²=5476 94²=8836 15²=225 35²=1225 55²=3025 75²=5625 95²=9025 16²=256 36²=1296 56²=3136 76²=5776 96²=9216 17²=289 37²=1369 57²=3249 77²=5929 97²=9049 18²=324 38²=1444 58²=3364 78²=6024 98²=9604 19²=361 39²=1521 59²=3481 79²=6241 99²=9081 20²=400 40²=1600 60²=3600 80²=6400 100²=10000