[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