Question

Using the Sutra Ekadhiken Poorvena, find the squares of the following numbers:
(i) 45
(ii) 85
(iii) 115

Answer 1

Hint: We will describe the Sutra Ekadhikena Purvena method for finding squares. This method is for numbers that have the digit 5 in the unit’s place. We will follow the described method step by step to obtain the squares for the given numbers. This method involves the multiplication of consecutive numbers excluding the unit digit of the given number.

Complete step by step answer:
The Sutra Ekadhiken Poorvena method for finding squares is as follows,
(1) We will check whether the number has the digit 5 in the unit’s place. If yes, then we will take the new number to be the old number excluding the unit digit 5.
(2) We will add 1 to the new number and multiply it to the new number.
(3) We will square the digit 5.
(4) We will write the product obtained in step two followed by the square obtained in step three. This number is the square of the given number.
Using this method, we will find the squares of the given numbers.
(i) 45
We can see that the unit’s place has the digit 5. So, our new number is 4. According to the next step, we have to multiply 4 at $ 4+1=5 $. The product is $ 4\times 5=20 $ . According to the third step, the square of 5 is 25. Therefore, we obtain the square of 45 to be 2025.
(ii) 85
This number has 5 in the unit’s place. Then, we get a new number as 8. The product of 8 and $ 8+1=9 $ is $ 8\times 9=72 $ . The square of 5 is 25. Therefore, the square of 85 is 7225.
(iii) 115
The unit’s place of the given number is 5. Next, we get a new number as 11. We have to multiply 11 and $ 11+1=12 $. The product is $ 11\times 12=132 $ . Hence, the square of 115 is 13225.

Note:
This method of finding squares works for numbers ending in 5. There are multiple methods of finding squares, for example, the diagonal method. The diagonal method works for all numbers, unlike the Sutra Ekadhikena Poorvena method. It is useful to be aware of such methods as they help us save time in calculations.