Answer:
(i) 525 We have
This shows that \[{{22}^{2}}<525\]. Next perfect square is \[{{23}^{2}}=529\]. Hence, the number to be added is \[{{23}^{2}}-525=529-525=4\]. Therefore, the perfect square so obtained is \[525+4=529\]. Hence, \[\sqrt{529}=23\]. (ii) 1750 We have 22 2 \[\overline{5}\] \[\overline{25}\] ?4 42 1 25 ? 84 41
This shows that \[{{41}^{2}}<1750\]. Next perfect square is \[{{42}^{2}}=1764\]. Hence, the number to be added is \[{{42}^{2}}-1750=1764-1750=14\] Therefore, the perfect square so obtained is \[1750+14=1764\]. Hence, \[\sqrt{1764}=42\]. (iii) 252 We have 41 4 \[\overline{17}\] \[\overline{50}\] ?16 81 1 50 ? 81 69
This shows that \[{{15}^{2}}<252\]. Next perfect square is \[{{16}^{2}}=256\]. Hence, the number to be added is \[{{16}^{2}}-252=256-252=4\]. Therefore, the perfect square so obtained is \[252+4=256\]. Hence, \[\sqrt{256}=16\]. (iv) 1825 We have 15 1 \[\overline{2}\] \[\overline{52}\] ?1 25 1 52 ?1 25 27
Thus shows that \[{{42}^{2}}<1825\]. Next perfect square is \[{{43}^{2}}=1849\]. Hence, the number to be added is \[{{43}^{2}}-1825=1849-1825=24\]. Therefore, the perfect square so obtained is \[1825+24=1849\]. Hence, \[\sqrt{1849}=43\]. (v) 6412 We have 42 4 \[\overline{18}\] \[\overline{25}\] ?16 82 2 25 ?1 64 61
This shows that \[{{80}^{2}}<6412\]. Next perfect square is \[{{81}^{2}}=6561\]. Hence, the number to be added is \[{{81}^{2}}-6412=6561-6412=149\]. Therefore, the perfect square so obtained is \[6412+149=6561\]. Hence, \[\sqrt{6561}\,=81\]. 80 8 \[\overline{64}\] \[\overline{12}\] ?64 160 12 ?0 12
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