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Question

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


Solution

(i) 5607

Finding the square root of 5607,we see that

742=5607131=5476 and 752=5625 5476<5607<5625 56255607=18 is to be added to a perfect a perfect square Least number to be added=18

(ii) 4931

 

Finding the square root of 4931 ,we see that

702=4900712=5041 4900<4931<5041 50414931=110 is to be added to a perfect square Least number to be added=110

(iii) 4515600

Finding the square root of 4515600,we see that 21242=4511376 and 21252=4515625

 4511376<4515600<4515625 45156254931=25 is to be added to a perfect square Least number to be added=25

(iv) 37460 

Finding the square root of 37460 ,we see that 1932=37249 and 1942=37636

 37249<37460<37636 3763637460=176 is to be added to a perfect square Least number to be added=176

(v) 506900

Finding the square root of 506900,we see that 7112=505521 and 7122=506944

 505521<506900<506944 506944506900=44 is to be added to a perfect square Least number to be added=44

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