how to find the squareroot of 1681
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41 is the square root of 1681.
proof :
i) By approximate method
find square number nearer to 1681. you know 40² = 1600
in the unit place of number is 1 so square root of must be ending with 1 or 9 (1 × 1 = 1 and 9 × 9 = 81)
so √1681 = 41 or 49
square of numbers ending with 5 e.g. 25²
make 5 × 5 = 25 write this in answer. Now add 1 to to remaining part (2 + 1) it is 3 and 3 × 2 = 6 write 6 before 25 and answer is 625
.g.(1+ 2) | 5
× 2 -------| 5
------------------
--- 6 ------- | 25
so 45² = (1 + 4)×4 and 25
answer is 2025
so 1600 < 1681 < 2025
so √1681 may be 41 confirm by multiplication.
proof :
i) By approximate method
find square number nearer to 1681. you know 40² = 1600
in the unit place of number is 1 so square root of must be ending with 1 or 9 (1 × 1 = 1 and 9 × 9 = 81)
so √1681 = 41 or 49
square of numbers ending with 5 e.g. 25²
make 5 × 5 = 25 write this in answer. Now add 1 to to remaining part (2 + 1) it is 3 and 3 × 2 = 6 write 6 before 25 and answer is 625
.g.(1+ 2) | 5
× 2 -------| 5
------------------
--- 6 ------- | 25
so 45² = (1 + 4)×4 and 25
answer is 2025
so 1600 < 1681 < 2025
so √1681 may be 41 confirm by multiplication.
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