Subjects number theory

Ones Digit Square Root Eccb74

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Ones Digit Square Root Eccb74


1. **Problem Statement:** Find the possible one's digits of the square roots of the given numbers: 9801, 059856, 998001, 657666025. 2. **Important Rule:** The one's digit of a perfect square can only be 0, 1, 4, 5, 6, or 9. To find the possible one's digit of the square root, we look for digits whose square ends with the given number's last digit. 3. **Step-by-step:** - For 9801: The last digit is 1. The digits whose square ends in 1 are 1 and 9 because $1^2=1$ and $9^2=81$. - For 059856 (which is 59856): The last digit is 6. The digits whose square ends in 6 are 4 and 6 because $4^2=16$ and $6^2=36$. - For 998001: The last digit is 1. Same as above, possible digits are 1 and 9. - For 657666025: The last digit is 5. The only digit whose square ends in 5 is 5 because $5^2=25$. 4. **Final answers:** - 9801: possible one's digits of square root are 1 or 9. - 059856: possible one's digits of square root are 4 or 6. - 998001: possible one's digits of square root are 1 or 9. - 657666025: possible one's digit of square root is 5.