What is a Square number?
When you multiply a whole number (or) Integer (not a fraction) by itself, the result is called the Square of that number.
Here are the Squares of 1 to 30 Numbers.,
SQARES 1 to 30 | ||
1 X 1 = 1 | 11 X 11 = 121 | 21 X 21 =441 |
2 X 2 = 4 | 12 X 12 = 144 | 22 X 22 = 484 |
3 X 3 = 9 | 13 X 13 = 169 | 23 X 23 = 529 |
4 X 4 = 16 | 14 X 14 = 196 | 24 X 24 = 576 |
5 X 5 = 25 | 15 X 15 = 225 | 25 X 25 = 625 |
6 X 6 = 36 | 16 X 16 = 256 | 26 X 26 = 676 |
7 X 7 = 49 | 17 X 17 = 289 | 27 X 27 = 729 |
8 X 8 = 64 | 18 X 18 = 324 | 28 X 28 = 784 |
9 X 9 = 81 | 19 X 19 = 361 | 29 X 29 = 841 |
10 X 10 = 100 | 20 X 20 = 400 | 30 X 30 = 900 |
Note:
1) If a number has 1 or 9 in its unit's place then its square ends with 1 in units place. (We can cross check it by above table).
2) Square of a even number is always even, and square of an odd number is always Odd.
Ex: 22 = 4, 62 = 36, 72 = 49, 92 = 81
3) Three natural numbers x, y, z is called a Pythagorean triplet if X2 + y2 = z2.
Ex: (3, 4, 5), (6, 8, 10), (7, 24, 25) etc.,
since 32 + 42 = 9 + 16 = 25, and 52.= 25
For any natural number 'n' which is greater than 1, the Pythagorean triplet is given by (2n, n2-1, n2+1 )
Ex: Find the other two Pythagorean triplets, one number which is 10.
Sol: For any natural number 'n' the Pythagorean triplet is = 2n, n2-1, n2+1
consider n as 5 as per given above
2n = 2 *5 = 10,
n2-1 = 52 - 1 = 25 - 1 = 24, and
n2+1 = 52 + 1 = 25 + 1 = 26.
So, the other two numbers are 24 and 26.
4) The square of a natural number 'n' is equal to the sum of the first n odd numbers.
Ex: Thus 12 = 1, sum of the first odd number,
22 = 4 = 1 + 3, sum of the first 2 odd numbers,
32 = 9 = 1 + 3 + 5, sum of the first 3 odd numbers,
42 = 16 = 1+3+5+7 =16, sum of the first 4 odd numbers, etc.,
5) For any natural number 'n' which is greater than 1, (n + 1) X (n - 1) = n2-1.
6) Finding the square of a number which is ending with 5 (last digit as 5) is as follows:
Ex: 252 = 2 X 3 = 6, 52 = 25 so the answer is 625.
What ever may be the earlier part (n), multiply it with one more than it self (n+1) that will become over answer's first part, the second part of the number will be 25 only.
352 = 3 X 4 = 12, 52 = 25 so the answer is 1225.
452 = 4 X 5 = 20, 52 = 25 so the answer is 2025.
552 = 5 X 6 = 30, 52 = 25 so the answer is 3025.
1352 = 13 X 14 = 182, 52 = 25 so the answer is 18225.
1552 = 15 X 16 = 240, 52 = 25 so the answer is 24025.
Square Root: