Determine the possible one's digits for the square root of each number.

Step 1: Determine the possible one's digits for the square root of each number.
The one's digit of a perfect square determines the possible one's digits of its square root.

• If the number ends in 1, the square root ends in 1 or 9.
• If the number ends in 4, the square root ends in 2 or 8.
• If the number ends in 5, the square root ends in 5.
• If the number ends in 6, the square root ends in 4 or 6.
• If the number ends in 9, the square root ends in 3 or 7.
• If the number ends in 0, the square root ends in 0.

• (i) 9801 The number 9801 ends in 1. The possible one's digits of its square root are $\boxed{1 \text{ or } 9}$.

• (ii) 99856 The number 99856 ends in 6. The possible one's digits of its square root are $\boxed{4 \text{ or } 6}$.

• (iii) 998001 The number 998001 ends in 1. The possible one's digits of its square root are $\boxed{1 \text{ or } 9}$.

• (iv) 657666025 The number 657666025 ends in 5. The possible one's digit of its square root is $\boxed{5}$.