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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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1 Answers

(i) 729 can be factorised as follows.

3 729
3 243
3 81
3 27
3 9
3 3
1

729 = 3 × 3 × 3 × 3 × 3 × 3

∴ √729 = 3 x 3 x 3 = 27

(ii) 400 can be factorised as follow.

2 400
2 200
2 100
2 50
2 25
5 5
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.

2 1764
2 882
3 441
3 147
7 49
7 7
1

1764 = 2 × 2 × 3 × 3 × 7 × 7

∴ √1764 = 2 x 3 x 7 = 42

(iv) 4096 can be factorised as follows.

2 4096
2 2048
2 1024
2 512
2 256
2 128
2 65
2 32
2 16
2 8
2 4
2 2
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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