Question

What could be the possible units place digit of the following square root of a number?
A.$9801$
B.$99856$
C.$99801$
D.$657666025$

Answer 1

Hint: Always while guessing the unit’s place digit after the operations like square or square root is done can be only analyzed by knowing the square of square root of the unit’s place digit.


Complete step-by-step answer:
$9801$
The given number is an odd number and the unit's place digit ends with $1$ which is also an odd number.
The square of only $1$ and $9$ yields $1$ at the unit’s place of the squared number. (Square of $1$ is $1$ while the square of $9$ is$81$ ).
Therefore, the unit’s place digit for the square root of $9801$ will be either $1$ or $9$ .

$99856$
The given number is an even number and unit’s place digit ends with $6$ which is also an even number.
The square of only $4$ and $6$ yields $6$ at the unit’s place of the squared number. (Square of $4$ is $16$ while the square of $6$ is$36$ ).
Therefore, the unit’s place digit for the square root of will be either or .

$99801$
The given number is an odd number and the unit's place digit ends with $1$ which is also an odd number.
The square of only $1$ and $9$ yields $1$ at the unit’s place of the squared number. (Square of $1$ is $1$ while the square of $9$ is$81$ ).
Therefore, the unit’s place digit for the square root of $99801$ will be either $1$ or $9$ .

$657666025$
The given number is an odd number and the unit's place digit ends with which is also an odd number.
The square of only $5$ yields $5$ at the unit’s place of the squared number. (Square of $5$ is $25$ ).
Therefore, the unit’s place digit for the square root of $657666025$ will be $5$ .


Note: The important point that should be kept in mind is that the unit's place digit for the square of the number’s from to should be remembered.
 Since only the unit’s place digit is to be determined therefore the change that will take place at the unit’s place after the operations like square or square root is done, should be analyzed.