Find the smallest number which must be added to each of the follow
numbers so as to get a perfect square number:
(1) 1442
(2) 2205
(3)3361
Answers
this is the pic of first question that is 1442
(1) 2 must be added to 1442 to make it perfect square that is 1444.
(2) 4 must be added to 2205 to make it perfect square that is 2209.
(3) 3 must be added to 3361 to make it perfect square that is 3364.
Solution:
We need to find what number must be added to each of following number to get perfect square number.
(1) 1442:
Square of 37 = 37 x 37 = 1369
Square of 38 = 38 x 38 = 1444
Clearly position of the given number is between squares of 37 and 38
That is 1369 < 1442 < 1444
So if we add 2 to 1442, it will become 1444 which is perfect square of 38.
Hence 2 must be added to 1442 to make it perfect square that is 1444.
(2) 2205:
Square of 46 = 46 x 46 = 2116
Square of 47= 47 x 47 = 2209
Clearly position of the given number is between squares of 46 and 47
That is 2116 < 2205 < 2209
So if we add 4 to 2205, it will become 2209 which is perfect square of 47.
Hence 4 must be added to 2205 to make it perfect square that is 2209.
(3) 3361:
Square of 58= 58 x 58 = 3364
Clearly position of the given number is between squares of 57 and 58
That is 3249< 3361< 3364
So if we add 3 to 3361, it will become 3364 which is perfect square of 58.
Hence 3 must be added to 3361 to make it perfect square that is 3364.