Question

What could be the possible 'one's' digits of the square root of each of the following numbers?

1. 9801
2. 99856
3. 998001
4. 657666025

Answer 1

(i) If the number ends with $1$, then the one's digit of the square root of that number may be $1$ or $9$.
Therefore, one's digit of the square root of $9801$ is either $1$ or $9$.

---

(ii) If the number ends with $6$, then the one's digit of the square root of that number may be $4$ or $6$.
Therefore, one's digit of the square root of $99856$ is either $4$ or $6$.

---

(iii) If the number ends with $1$, then the one's digit of the square root of that number may be $1$ or 9.
Therefore, one's digit of the square root of $998001$ is either $1$ or $9$.

---

(iv) If the number ends with $5$, then the one's digit of the square root of that number will be $5$.
Therefore, the one's digit of the square root of $657666025$ is $5$.