Answer:
(i) 402 We have
This shows that 202 is less than 402 by 2. This means, if we subtract the remainder from the number, we get a perfect square. So, the required least number is 2. Therefore, the required perfect square is \[402-2=400\] Hence, \[\sqrt{400}=20\]. (ii) 1989 We have 2 0 2 \[\overline{4}\] \[\overline{02}\] ?4 40 02 ?00 0
This shows that \[{{44}^{2}}\] is less than 1989 by 53. This means that if we subtract the remainder from the number, we get a perfect square. So, the required least number is 53. Therefore, the required perfect square is 1989 - 53 = 1936. Hence, \[\sqrt{1936}=44\]. (iii) 3250 We have 4 4 4 \[\overline{19}\] \[\overline{89}\] ?16 84 3 89 ?3 36 53
This shows that \[{{57}^{2}}\] is less than 3250 by 1. This means if we subtract the remainder from the number, we get a perfect square. So, the required least number is 1. Therefore, the required perfect square is \[3250-1=3249\] Hence, \[\sqrt{3249}\,=57\]. (iv) 825 We have 5 7 5 \[\overline{32}\] \[\overline{50}\] ?25 107 7 50 ?7 49 1
This shows that 282 is less than 825 by 41. This means if we subtract the remainder from the number, we get a perfect square. So, the required least number is 41. Therefore, the required perfect square is \[825-41=784\] Hence, \[\sqrt{784}=28\]. (v) 4000 We have 2 8 2 \[\overline{8}\] \[\overline{25}\] ?4 48 4 25 ?3 84 41
This shows that 632 is less than 4000 by 31. This means if we subtract the remainder from the number, we get a perfect square. So, the required least number is 31. Therefore, the required perfect square is \[4000-31=3969\]. Hence, \[\sqrt{3969}=63\]. 63 2 \[\overline{40}\] \[\overline{00}\] ?36 123 4 00 ?3 69 31
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