Find the least number which must be added to the following numbers to make them a perfect square:
(i) 5607
(ii) 4931
(iii) 4515600
(iv) 37460
(v) 506900

To do:

We have to find the least number which must be added to the given numbers to make them a perfect square.

Solution:

(i) Square root of 5607 is,

$74^2<5607$

$75^2=5625$

This implies,

$74^2<5607<5625$

Therefore,

$5625 - 5607 = 18$ has to be added to get a perfect square.

The least number which must be added to 5607 to make it a perfect square is 18. 

(ii) Square root of 4931 is,

$70^2<4931$

$71^2=5041$

This implies,

$70^2<4931<5041$

Therefore,

$5041 - 4931 = 110$ has to be added to get a perfect square.

The least number which must be added to 4931 to make it a perfect square is 110. 

(iii) Square root of 4515600 is,

$2124^2<4515600$

$2125^2=4515625$

This implies,

$2124^2<4515600<2125^2$

Therefore,

$4515625 - 4515600 =25$ has to be added to get a perfect square.

The least number which must be added to 4515600 to make it a perfect square is 25. 

(iv) Square root of 37460 is,

$193^2<37460$

$194^2=37636$

This implies,

$193^2<37460<194^2$

Therefore,

$37636 - 37460 =176$ has to be added to get a perfect square.

The least number which must be added to 37460 to make it a perfect square is 176. 

(v) Square root of 506900 is,

$711^2<506900$

$712^2=506944$

This implies,

$711^2<506900<712^2$

Therefore,

$506944 - 506900 =44$ has to be added to get a perfect square.

The least number which must be added to 506900 to make it a perfect square is 44. 

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Updated on: 10-Oct-2022

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