Question

What could be possible one's digit of the square root of each of the following numbers?
A) $9801$
B) $99856$
C) $998001$
D) $657666025$

Answer 1

Hint: In order to solve this question we have to check the square of the number that is present in the unit place of the number.

Complete step-by-step answer:
A) Solution for $9801$
In the given number $9801$, $1$is in the unit place so we have to check the square number of $1$, that is,${1^2} = 1$. Now we have to check other numbers whose square number has one in the unit place, that number is $9$ because ${9^2} = 81$. So the possible one’s digit must be either $1$ or $9$
1 and 9 are the possible one’s digit.
B) Solution for $99856$
In the given number $99856$, $6$ is in the unit place so we have to check the square number of ${6^2} = 36$. Now we have to check other numbers whose square number has six in the unit place, that number is ${4^2} = 16$. So the possible one’s digit must be either $4$ or $6$
4 and 6 are the possible one’s digit.
C) Solution for $998001$
In the given number $998001$, $1$ is in the unit place so we have to check the square number of $1$, that is,${1^2} = 1$. Now we have to check other numbers whose square number has one in the unit place, that number is $9$ because ${9^2} = 81$. So the possible one’s digit must be either $1$ or $9$
1 and 9 are the possible one’s digit.
D) Solution for $657666025$
In the given number $657666025$, $5$ is in the unit place so we have to check the square number of $5$ that is $25$. Now we have to check other numbers whose square number has $5$ in the unit place, but there is no such number except $5$ whose square number has $5$ in the unit place.
5 is the possible one’s digit.

Note: It is to be noted that the unit place digit must be from $1$ to $9$ as it is a single digit so one must calculate the square of those digits. In many cases it happens that students also check other digits $10$, $11$ or any other number which is not needed and it is time-consuming too and for this calculation mistakes might take place.