Page 85 - Start Up Mathematics_8 (Non CCE)

4 913,
3
(b) 3 -0 004913. = - 0 004913. = - 3
10 00 000, , 17 4,913
- 4 913, 17 289
3
=
3 10 00 000, , 17 17
1
4,913 = 17 × 17 × 17

3
\ 4913 = 3 17 17 17¥ ¥ = 17
10,00,000 = 100 × 100 × 100

\ 10 00 000, , = 3 100 100 100¥ ¥ = 100
3
- 4 913, -17
3
3
\ -0 004913. = = =-017.
3 10 00 000, , 100
Example 17: Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 0.098784. Find the
numbers.
Solution: Let the three numbers be x, 2x and 3x.
3
3
3
Then x + (2x) + (3x) = 0.098784 2 2,744
3
3
3
fi x + 8x + 27x = 0.098784 2 1,372
3
fi 36x = 0.098784 2 686
3
fi x = 0 098784. = 98 784, = 2 744, 7 343
36 36 10 00 000, , 10 00 000, , 7 49
¥
7 7
2 744, 3 2 744,
fi x = 3 = 1
10 00 000, , 3 10 00 000, ,
7
2
7
2
3 2 ¥¥¥¥¥ 7 2 ¥ 7 14
= = = = 014.
3 100 100 100¥ ¥ 100 100
\ The three numbers are 0.14, 2 × 0.14 and 3 × 0.14, i.e., 0.14, 0.28 and 0.42
EXERCISE 4.4
1. Find the cube roots of the following:
(a) –343 (b) –40,96,000 (c) –6,859 (d) –3,73,248 (e) 2.197
(f) –0.729 (g) 0.039304 (h) –0.005832

2. Prove that:
(a) 3 8 ¥ 3 27 = 3 8 ¥ 27 (b) 3 125 ¥ 3 216 = 3 125 ¥ 216

(c) 3 -512 ¥ 343 =-512 ¥ 343 (d) 3 -729 ¥ -1 000(, ) = -729 ¥ -1 000,
3
3
3
3
3. Evaluate the following:
3
¥
(a) 3 81 331¥ , (b) -125 729 (c) -64 ¥ -343( ) (d) 6 ¥ 8 3
3
3
3
125 8 0 729. 009.
6
6
3
(e) 125 p - 3 125p (f) 1 331, + 3 0 027. - 3 0 008. (g) 3 512 ¥ 5 (h) 3 4 096. ∏ 016.
3
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