write the next two square number after441 which end in 1 and their corresponding number?
Answers
Question :- write the next two square number after441 which end in 1 and their corresponding number ?
Solution :-
concept for unit digit of s square number :-
→ 1² = 1 = unit digit 1 .
→ 2² = 4 = unit digit 4.
→ 3² = 9 = unit digit 9.
→ 4² = 16 = unit digit 6.
→ 5² = 25 = unit digit 5.
→ 6² = 36 = unit digit 6 .
→ 7² = 49 = unit digit 9.
→ 8² = 64 = unit digit 4.
→ 9² = 81 = unit digit 1.
→ 10² = 100 = unit digit 0.
So, unit digit of a square number is depends on the unit digit of digit of square root of that number..
Conclusion :-
- unit digit 1 in last = 1 or 9.
- unit digit 4 in last = 2 or 8.
- unit digit 6 in last = 4 or 6.
- unit digit 9 in last = 3 or 7.
- unit digit 5 in last = 5
- unit digit 0 in last = 0 .
Therefore, next two square numbers end unit digit 1 will either have 1 or 9 as unit digit of their square root.
we know that, 441 is square of 21.
So,
→ Next number after 21 , that gives unit digit 1 = 29
→ Next number after 29 , that gives unit digit 1 = 31
Hence,
→ Square of 29 = 29 * 29 = 841 (Ans.)
→ Square of 31 = 31 * 31 = 961 (Ans.)
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