  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=5607−131=5476 and 752=5625∵ 5476<5607<5625∴ 5625−5607=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∴ 5041−4931=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∴ 4515625−4931=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∴ 37636−37460=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∴ 506944−506900=44 is to be added to a perfect square∴ Least number to be added=44  Suggest corrections   