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Question

Find the square root of the following number by prime factorisation method
(i) 729
(ii) 400
(iii) 1764
(iv) 4096
(v) 7744
(vi) 9604
(vii) 5929
(viii) 9216
(ix) 529
(x) 8100

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Solution

(i) 729

3729324338132739331

729=3×3×3×3×3×3= 32×32×32
729=27
(ii) 400

240022002100250525551

400=22×22×52
400=20
(iii) 1764

21764288234413147749771

1764=22×32×72
1764=42
(iv) 4096

2409622048210242512225621282642322162824221

1764=22×22×22×22×22×22
4096=64
(v) 7744

2774423872219362968248422421112111111

7744=22×22×22×112
7744=88
(vi) 9604

2960424802724017343749771

9604=22×72×72

9604=98
(vii) 5929

7592978471112111111

5929=112×72
5929=77
(viii) 9216

2921624608223042115225762288214427223621839331

9216=22×22×22×22×22×32

9216=962
9216=96
(ix) 529

2352923231

529=23×23=232
529=23
(x) 8100

281002405052025540538132739331

8100=22×32×32×52

8100=902

8100=90.


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