Question

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

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

Answer 1

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

Answer 2

(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