Question

What could be the possible ‘one’s’ digits of the square root of each of the following numbers?
A. 9801
B. 99856
C. 998001
D. 657666025

Answer 1

Hint: We will first find the one’s digit of each of the squares of the numbers from 0 to 9. We will then analyse each of the given numbers one digit one by one and find the possible one digit of the square root of that number.

Complete step-by-step answer:
 In this question, we have been given some numbers and are asked to find the unit’s place digit of the square root of each of the given numbers that can be possible. The numbers given in the question are, 9801, 99856, 998002, 657666025. Before proceeding to check the same for each of the numbers, we will first check the one’s or the unit’s digit of the squares of the numbers from 0 to 9. For that, we will first take the square of each of the numbers from 0 to 9.
So, for digit 0, the square is $0\times 0$ or 0 and its unit digit is 0.
For digit 1, the square is $1\times 1$ or 1 and its unit digit is 1.
For digit 2, the square is $2\times 2$ or 4 and its unit digit is 4.
For digit 3, the square is $3\times 3$ or 9 and its unit digit is 9.
For digit 4, the square is $4\times 4$ or 16 and its unit digit is 6.
For digit 5, the square is $5\times 5$ or 25 and its unit digit is 5.
For digit 6, the square is $6\times 6$ or 36 and its unit digit is 6.
For digit 7, the square is $7\times 7$ or 49 and its unit digit is 9.
For digit 8, the square is $8\times 8$ or 64 and its unit digit is 4.
For digit 9, the square is $9\times 9$ or 81 and its unit digit is 1.
Now, we will analyse each of the given numbers one’s or unit’s digit and find its square roots one’s digit.
A. So, for 9801, the one’s digit is 1. Now we have obtained that for the unit’s digit to be 1, only the squares of 1 and 9 can have one’s digit as 1.
Thus, for 9801, the possibilities are 1 and 9.
B. For 99856. Its one’s digit is 6. We know that for the last digit to be 6, only the squares of 4 and 6 can have the last one’s digit as 6.
Thus, for 99856, the possibilities are 4 and 6.
C. For 998001, the one’s digit is 1. So, as we know for the unit’s digit to be 1, only the squares of 1 and 9 can have one’s digit as 1.
Thus, for 998001, the possibilities are 1 and 9.
D. For 657666025, the one’s digit is 5. Now, for the last digit to be 5, only the squares of 5 can have the last digit as 5.
Thus, for 657666025, the only possibility is 5.

Note: Sometimes the one’s digit is also called as the unit’s digit, so the students should be aware of this fact and not get confused by the terms. One should also remember that the one’s digit is the last digit of a number when seen from left to right. The students sometimes forget to check the other possible values of the one’s digit of the square after they have found one possible value. For example, if the one’s digit of a number is 9, then its square root’s one’s digit may be 3 or 7 and missing any of these values will make the answer incorrect.