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Find the square roots of the following numbers by the Prime Factorisation Method.

(i) 729  (ii) 400  (iii) 1764  (iv) 4096

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(i) 729  (ii) 400  (iii) 1764  (iv) 4096

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(i) 729 can be factorised as follows.

3729
3243
381
327
39
33
1

729 = 3 × 3 × 3 × 3 × 3 × 3

∴ √729 = 3 x 3 x 3 = 27

(ii) 400 can be factorised as follow.

2400
2200
2100
250
225
55
1

400 = 2 x 2 x 2 x 2 x 5 x 5

∴ √400 = 2 x 2 x 5 = 20

(iii) 1764 can be factorised as follows.

21764
2882
3441
3147
749
77
1

1764 = 2 × 2 × 3 × 3 × 7 × 7

∴ √1764 = 2 x 3 x 7 = 42

(iv) 4096 can be factorised as follows.

24096
22048
21024
2512
2256
2128
265
232
216
28
24
22
1

4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

∴ √729 = 2 x 2 x 2 x 2 x 2 x 2 = 64

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