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

Answer 1

(i) 5607

Finding the square root of 5607,we see that

${74}^2=5607-131=5476and{75}^2=5625\because 5476<5607<5625\therefore 5625-5607=18istobeaddedtoaperfectaperfectsquare\therefore Leastnumbertobeadded=18$

(ii) 4931

Finding the square root of 4931 ,we see that

${70}^2=4900{71}^2=5041\therefore 4900<4931<5041\therefore 5041-4931=110istobeaddedtoaperfectsquare\therefore Leastnumbertobeadded=110$

(iii) 4515600

Finding the square root of 4515600,we see that ${2124}^2=4511376and{2125}^2=4515625$

$\therefore 4511376<4515600<4515625\therefore 4515625-4931=25istobeaddedtoaperfectsquare\therefore Leastnumbertobeadded=25$

(iv) 37460

Finding the square root of 37460 ,we see that ${193}^2=37249and{194}^2=37636$

$\therefore 37249<37460<37636\therefore 37636-37460=176istobeaddedtoaperfectsquare\therefore Leastnumbertobeadded=176$

(v) 506900

Finding the square root of 506900,we see that ${711}^2=505521and{712}^2=506944$

$\therefore 505521<506900<506944\therefore 506944-506900=44istobeaddedtoaperfectsquare\therefore Leastnumbertobeadded=44$