# Square Numbers: Multiplying With The Same Number

What are square numbers ?

When a number is multiplied by itself, the product is called as a ‘Square Number’.

Why Square Numbers:

As squares have all the sides equal, in a similar manner a square number is the product of two number which are equal (i.e. the number itself).

Area of a square = Side $\times$ Side

Square number = a $\times\; a \; = a^{2}$

 Side of square (in cm) Area of square (in cm2) 3 3 × 3 = $3^{2}$ = 9 5 5 × 5 = $5^{2}$ = 25 7 7 × 7 = $7^{2}$ = 49 8 8 × 8 = $8^{2}$ = 64

Numbers such as 1, 4, 9, 16, 25, 36, 49, 64, etc. are special numbers as these are the product of a number by itself.

If we express a number (x) in terms of square of any natural number such as a2, then x is a square number. For example 100 can be expressed as 10 × 10 = 102, where 10 is a natural number, therefore 100 is a square number. Whereas, the number 45 cannot be called as a square number because it is the product of numbers 9 and 5. The number is not multiplied by itself. Square numbers can also be called as perfect square numbers.

List of squares for numbers less than 602 = 3600

 02 = 0 102 = 100 202 = 400 302 = 900 402 = 1600 502 = 2500 12 = 1 112 = 121 212 = 441 312 = 961 412 = 1681 512 = 2601 22 = 4 122 = 144 222 = 484 322 = 1024 422 = 1764 522 = 2704 32 = 9 132 = 169 232 = 529 332 = 1089 432 = 1849 532 = 2809 42 = 16 142 = 196 242 = 576 342 = 1156 442 = 1936 542 = 2916 52 = 25 152 = 225 252 = 625 352 = 1225 452 = 2025 552 = 3025 62 = 36 162 = 256 262 = 676 362 = 1296 462 = 2116 562 = 3136 72 = 49 172 = 289 272 = 729 372 = 1369 472 = 2209 572 = 3249 82 = 64 182 = 324 282 = 784 382 = 1444 482 = 2304 582 = 3364 92 = 81 192 = 361 292 = 841 392 = 1521 492 = 2401 592 = 3481

## Odd and Even square numbers

• Squares of even numbers are even, i.e, (2n)2 = 4n2.
• Squares of odd numbers are odd, i.e, (2n + 1) = 4(n2 + n) + 1.
• Since every odd square is of the form 4n + 1, the odd numbers that are of the form 4n + 3 are not square numbers.

## Special Properties of square numbers

Here we have covered square numbers and their properties, you can refer completing the square method which by following the link provided. To learn more about other topics download BYJU’S – The Learning App and learn the subjects in an intereactive and innovative ways.

#### Practise This Question

Find x in x29=72.