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Question

Find the square roots of the following numbers by the 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 can be factorized as follows.

3729324338132739331

729=3×3×3×3×3×3

=32×32×32

729=3×3×3=27

(ii) 400 can be factorized as follows.

240022002100250525551

400=2×2×2×2×5×5

=22×22×52

400=2×2×5=20

(iii) 17264 can be factorized as follows.

21764288234413147749771

17264=2×2×3×3×7×7

=22×32×72

1764=2×3×7=42

(iv) 4096 can be factorized as follows.

2409622048210242512225621282642322162824221

4096=2×2×2×2×2×2×2×2×2×2×2×2

=22×22×22×22×22×22

1764=2×2×2×2×2×2=64

(v) 7744 can be factorized as follows.

2774423872219362968248422421112111111

7744=2×2×2×2×2×2×11×11

=22×22×22×112

1764=2×2×2×11=88

(vi) 9604 can be factorized as follows.

2960424802724017343749771

9604=2×2×7×7×7×7

=22×72×72

9604=2×7×7=98

(vii) 5929 can be factorized as follows.

7592978471112111111

5929=7×7×11×11

=72×112

5929=7×11=77

(viii) 9216 can be factorized as follows.

2921624608223042115225762288214427223621839331

9216=2×2×2×2×2×2×2×2×2×2×3×3

=22×22×22×22×22×32

5929=2×2×2×2×2×3=96

(ix) 529 can be factorized as follows.

2352923231

529=23×23

=232

529=23

(x) 8100 can be factorized as follows.

28100240503202536753225375525551

8100=2×2×3×3×3×3×5×5

=22×32×33×52

529=2×3×3×5=90


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