441
(i) Unit place digit of 441 is 1. Therefore 441 may be a perfect square number.
(ii) Sum of digit of 441 = 4 + 4 + 1 = 9 which is perfect square.
(iii) There may be two digits in square root of 441.
(iv) Making pair of 2 – 2 digits from right to left, second pair has only one digit 4. Therefore tens place digits in square root will be 2.
(v) Extreme digit of number is 1.
Therefore extreme digit in square root will be either 1 or 9 and for tens place is 2 which belongs a group 1 – 3 so the tens place will be 1.
(vi) Thus square root of 441 may be either 21 or 29.
(vii) On multiplying 2 with (2+1=3)
2 x 3 = 6
Here 4 digit of second pair < Product 6
∴ Smaller number out of 21 or 29 will be taken as square root
Hence square root of 441 = 21
