Hint: The unit digit of the square root with either 3 or 7. The first two digits can have a square root greater than or equal to 3. The square root can be 33 or 37, but the square of 35 is 1225 so it can’t be 33.
Complete step-by-step answer:
We need to predict the square root of 1369 using the Vilokanam method.
According to this method, we predict the square root of 3 or 4 digit numbers by observing the number.
The unit digit can help in predicting the last digit of the square root. The ten’s digit is predicted by first thousands digit and hundreds digit.
Let’s observe the number 1369. The unit digit is 9. The square of both 3 and 7 has a unit digit equal to 9. So, the unit digit of square root can be either 3 or 7.
Now, the thousands and hundreds digits are 1 and 3. The square of 3 is 9 and 4 is 16. As, 13 is less than 16, so it can’t be the first digit of square root. Hence, we have 3 as the ten’s digit of the square root.
Till now, we have 3 as tens digit of square root and either 3 or 7 as one’s digit of the square root i.e. 33 or 37 is the number.
But the square of 35 is 1225 which is less than 1369 that means the square 33 will be less than 1225 and hence less than 1369. So, the answer is 37.
Note: In these types of questions, we just need to follow the steps of Vilokanam method. Any perfect square can’t have 2 ,3 , 7 or 8 as a unit digit.