Squares of numbers ending in 1 & 5 by Bhārati Kṛṣṇa Tīrtha
A number, when multiplied by the number itself the product obtained, is called "Square of that number ". We will come to know the squares for numbers ending in a particular digit 5 , 1.
Squares of Numbers ending in 5[1]
To find the square of any number ending in 5 , the sūtra used is
एकाधिकेन पूर्वेण
" Ekādhikena Pūrveṇa "
" By one more than the one before "
Example : 352
| Left Hand Side (LHS) | Right Hand Side (RHS) |
|---|---|
| 3 | 5 |
| Previous digit of 5 in 35 is 3
one more than 3 is 4 |
Square of 5 = 25 |
| 3 X 4 = 12 | |
| 12 | 25 |
Right hand side will always be 25
Answer : 352 = 1225
Example : 1352
| Left Hand Side (LHS) | Right Hand Side (RHS) |
|---|---|
| 13 | 5 |
| Previous digit of 5 in 135 is 13
one more than 13 is 14 |
Square of 5 = 25 |
| 13 X 14 = 182 | |
| 182 | 25 |
Right hand side will always be 25
Answer : 1352 = 18225
Squares of Numbers ending in 1
The specific rule to be followed to find the square of a number ending in 1 is explained through the below examples.
Example : 312
| Left Hand Side (LHS) | Right Hand Side (RHS) |
|---|---|
| 3 | 1 |
Step 1: RHS : will always be 1 as (RHS)2 , 12 = 1
Step 2 : Middle: double the previous part of the number ( LHS) which is 3 . 3 X 2 = 6
Step 3 : LHS : Square of the previous part of the number (LHS) which is 3. 32 = 9
Step 4: Put the above values in the below table.
| LHS | MIddle | RHS |
|---|---|---|
| 9 | 6 | 1 |
Answer : 312 = 961
Example : 612
| Left Hand Side (LHS) | Right Hand Side (RHS) |
|---|---|
| 6 | 1 |
Step 1: RHS : will always be 1 as (RHS)2 , 12 = 1
Step 2 : Middle: double the previous part of the number ( LHS) which is 6 . 6 X 2 = 12
Step 3 : LHS : Square of the previous part of the number (LHS) which is 6. 62 = 36
Step 4: Put the above values in the below table.
| LHS | Middle | RHS |
|---|---|---|
| 36 | 12 | 1 |
| 36 | Put 2 and carry over 1 | 1 |
| 36 + Carry over 1 | 2 | 1 |
| 37 | 2 | 1 |
Answer : 612 = 3721
Example : 4512
| Left Hand Side (LHS) | Right Hand Side (RHS) |
|---|---|
| 45 | 1 |
Step 1: RHS : will always be 1 as (RHS)2 , 12 = 1
Step 2 : Middle: double the previous part of the number ( LHS) which is 45. 45 X 2 = 90
Step 3 : LHS : Square of the prev us part of the number (LHS) which is 45. Here the number ending in 5 we will use एकाधिकेन पूर्वेण sūtra
| Left Hand Side (LHS) | Right Hand Side (RHS) |
|---|---|
| 4 | 5 |
| Previous digit of 5 in 45 is 4
one more than 4 is 5 |
Square of 5 = 25 |
| 4 X 5 = 20 | |
| 20 | 25 |
LHS : 452 = 2025
Step 4: Put the above values in the below table.
| LHS | Middle | RHS |
|---|---|---|
| 2025 | 90 | 1 |
| 2025 | Put 0 and carry over 9 | 1 |
| 2025 + Carry over 9 | 0 | 1 |
| 2034 | 0 | 1 |
Answer : 4512 = 203401
See Also
1 और 5 से समाप्त होने वाली संख्याओं का वर्ग - भारती कृष्ण तीर्थ
References
- ↑ Singhal, Vandana (2007). Vedic Mathematics For All Ages - A Beginners' Guide. Delhi: Motilal Banarsidass. pp. 193–203. ISBN 978-81-208-3230-5.
