Squares of numbers near 100, 1000 or 50 (Yavadunam method)

100, 1000 या 50 के पास की संख्याओं का वर्ग (यावदूनम् विधि)

Square 97, 104 or 996 without long multiplication: add or subtract the difference from the base, then write the square of the difference after it.

आधार (100, 1000) से अंतर निकालें, संख्या में वही अंतर जोड़ें/घटाएं और अंत में अंतर का वर्ग लिखें।

Numbers just below or above 100

Find how far the number is from 100. Call this the difference d (negative if below 100).

Left part: number + d (so 97 becomes 97 − 3 = 94).
Right part: d², written with two digits because the base 100 has two zeros (9 becomes 09).
Join the two parts.

Example 97²

d = −3 → left 97 − 3 = 94, right (−3)² = 09 → 9409

Example 104²

d = +4 → left 104 + 4 = 108, right 16 → 10816

Example 112²

d = +12 → left 124, right 144 has three digits, so carry the 1: 124 + 1 = 125 | 44 → 12544

Example 89²

d = −11 → left 78, right 121 → carry 1 → 79 | 21 → 7921

Same rule, but the right part has three digits because 1000 has three zeros.

Example 996²

d = −4 → 992 | 016 → 992016

Example 1007²

d = +7 → 1014 | 049 → 1014049

For numbers near 50, work with base 100 and halve the left part.

Example 48²

d = −2 → (48 − 2) ÷ 2 = 23, right 04 → 2304

Example 53²

d = +3 → (53 + 3) ÷ 2 = 28, right 09 → 2809