Math, asked by sainasavlasiya, 1 year ago

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

Answered by ramesh0841
3

this is the pic of first question that is 1442

Attachments:
Answered by sharonr
3

(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.

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