Question

What could be possible one's digit of the square root of each of the following numbers?
(i) 9801
(ii) 99856
(iii) 998001
(iv) 657666025

Answer 1

(i) $9801$

Observe that the numbers ending with $1$ and $9$ are the only numbers whose square numbers end with $1$

$1^2=1$ and $9^2=81$

Since the last digit of $9801$ is $1$, the possible one's digit of it's square root can be $1$ or $9$.

(ii) $99856$

Observe that the numbers ending with $4$ and $6$ are the only numbers whose square numbers end with $6$

$4^2=16$ and $6^2=36$

Since the last digit of $99856$ is $6$, the possible one's digit of it's square root can be $4$ or $6$.

(iii) $998001$

Observe that the numbers ending with $1$ and $9$ are the only numbers whose square numbers end with $1$

$1^2=1$ and $9^2=81$

Since the last digit of $998001$ is $1$, the possible one's digit of it's square root can be $1$ or $9$.

(iv) $657666025$

Observe that the numbers ending with $5$ are the only numbers whose square numbers end with $25$

$5^2=25$

Since the last two digits of $657666025$ are $25$, the possible one's digit of it's square root can be $5$.