على سبيل المثال، 9 هو مربع كامل لأنه يساوي 3 × 3.:02 = 0:12 = 1:22 = 4:32 = 9:42 = 16:52 = 25:62 = 36:72 = 49:82 = 64:92 = 81:102 = 100:112 = 121:122 = 144:132 = 169:142 = 196:152 = 225:162 = 256:172 = 289:182 = 324:192 = 361:202 = 400:212 = 441:222 = 484:232 = 529:242 = 576:252 = 625:262 = 676:272 = 729:282 = 784:292 = 841:302 = 900:312 = 961:322 = 1024:332 = 1089:342 = 1156:352 = 1225:362 = 1296:372 = 1369:382 = 1444:392 = 1521:402 = 1600:412 = 1681:422 = 1764:432 = 1849:442 = 1936:452 = 2025:462 = 2116:472 = 2209:482 = 2304:492 = 2401:502 = 2500:512 = 2601:522 = 2704:532 = 2809:542 = 2916:552 = 3025:562 = 3136:572 = 3249:582 = 3364:592 = 3481* إذا كان عدد ما يكتب على شكل m5 (أي أن رقم وحداته هو 5)، فإن مربعه يكتب على شكل n25 حيث formula_1.
==Examples==The squares smaller than 602 are::02 = 0:12 = 1:22 = 4:32 = 9:42 = 16:52 = 25:62 = 36:72 = 49:82 = 64:92 = 81:102 = 100:112 = 121:122 = 144:132 = 169:142 = 196:152 = 225:162 = 256:172 = 289:182 = 324:192 = 361:202 = 400:212 = 441:222 = 484:232 = 529:242 = 576:252 = 625:262 = 676:272 = 729:282 = 784:292 = 841:302 = 900:312 = 961:322 = 1024:332 = 1089:342 = 1156:352 = 1225:362 = 1296:372 = 1369:382 = 1444:392 = 1521:402 = 1600:412 = 1681:422 = 1764:432 = 1849:442 = 1936:452 = 2025:462 = 2116:472 = 2209:482 = 2304:492 = 2401:502 = 2500:512 = 2601:522 = 2704:532 = 2809:542 = 2916:552 = 3025:562 = 3136:572 = 3249:582 = 3364:592 = 3481The difference between any perfect square and its predecessor is given by the identity formula_3.