Question

Find the square root of 961 using Vilokanam method.
(a) 29
(b) 30
(c) 31
(d) 32

Answer 1

Hint: In Vilokanam method, to find the square root of any digit, first of all we have to determine its digit in the unit's place, based on that the unit’s place of square root can be determined. Now, by ignoring another digit of the number given we will consider only the first digit and find the square root of that number or nearest possible maximum whose square is less than the obtained number. Then by rearranging the terms and finding the nearest unique number we will consider the square of that number and then if the square is less than the given number, we will consider it as an answer.

Complete step by step solution:
To find the square root of 961 using the Vilokanam method, first of all we will find the unit’s digit of the number, here it is 1. So, as per Vilokanam method the unit place of square root of 961 will be, 1.
Now, to find another digit, we will ignore the last two digits, so our digit will be 9. Now, the largest number whose square will be less than or equal to 9 is 3.
Now, from this we can say that we have 2 digits for the unit's place i.e. 1 and 9 and the ten’s place will be allotted to 3.
So as per the we have two numbers 31 and 39 now, the unique number which with unit digit 5 and lying between 31 and 39 can be given as, 35.
So, a square of 35 can be given as, ${{\left( 35 \right)}^{2}}=1225$. Now, if the number given in the question is bigger than 1225 then square root will be 39 and if the number is less than 1225, then the square root will be 31.
So, on comparing we can see that $961<1225$. So, the answer will be 31.
Thus, the square root of 961 is 31.
Hence, option (c) is the correct answer.

Note: Here, in unit’s place we were given 1, if it was given 4 as unit digit in number then our unit digit in square root will be 4 or 8 as per the Vedic math’s rule, if student will not know the rules then he won’t be able to solve further. So, students must learn the rules of Vedic maths to solve such problems easily.