Page 78 - Start Up Mathematics_8 (Non CCE)

1
Example 7: Find the cubes of: (a) 2 (b) -9 (c) 5.2
3 8

Ê 1ˆ 3 Ê 7ˆ 3
Solution: (a) Á 2 3¯ = Á ˜ (Changing into proper fraction)
˜
3¯
Ë
Ë
Ê ˆ 7 3 7 ¥ 7 ¥ 7 343
\ Á ˜ = =
3
Ë ¯ 3 3 ¥¥ 3 27
(
(
Ê - ˆ 9 3 ( -9) ¥ -9) ¥ -9) -729
(b) Á ˜ = 8 ¥¥ 8 = 512
¯
Ë 8
8
3
(c) (5.2) = 5.2 × 5.2 × 5.2 = 140.608
Alternatively,
52ˆ
3
(5.2) = Ê 10¯ 3 = 52 ¥ 52 ¥ 52 = 140 608, 1 000, , = 140 608.
Á
˜
Ë
¥
¥
10 10 10
-125
Example 8: Show as the cubes of a rational number: (a) (b) 0.046656
5 832,
3
Solution: (a) 125 = (5) fi –125 = (–5) 3 2 5,832
Writing 5,832 as a product of its prime factors, we get 2 2,916
5,832 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 2 1,458
3 729
3
3
3
3
= 2 × 3 × 3 = (2 × 3 × 3) = (18) 3 3 243
\ 5,832 = (18) 3 3 81
-125 ( -5) 3 Ê - ˆ 5 3 3 27
Hence, = = Á ˜ 3 9
,
5 832 () 3 Ë 18 ¯
18
3 3
-125 Ê - ˆ 5
So, is the cube of the rational number Á ˜ . 1
5 832, Ë 18 ¯
46 656,
(b) 0.046656 = 2 46,656 2 10,00,000
10 00 000, ,
2 23,328 2 5,00,000
2 11,664 2 2,50,000
2 5,832 2 1,25,000
2 2,916 2 62,500
2 1,458 2 31,250
3 729 5 15,625
3 243 5 3,125
3 81 5 625
3 27 5 125
3 9 5 25
3 3 5 5
1 1

70