Page 82 - Start Up Mathematics_8 (Non CCE)

(c) Units digit of the number = 7
fi Units digit of the cube root of the number = 3
The number left after striking out the units, tens and hundreds digits of 5,71,787 is 571.
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 8 < 571 < 9 3
fi The tens digit of the cube root of the number = 8
 571 787,, = 83
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EXERCISE 4.3
1. Find the smallest numbers by which the following numbers must be multiplied to make them perfect
cubes:
(a) 36,000 (b) 3,456 (c) 4,116
(d) 10,976 (e) 8,232
2. Find the smallest numbers by which the following numbers must be divided to make them perfect
cubes.
(a) 8,640 (b) 2,662 (c) 27,648
(d) 77,760 (e) 69,120
3. Find the cube roots of the following by prime factorization:

(a) 729 (b) 4,096 (c) 5,832
(d) 15,625 (e) 27,000 (f) 39,304
(g) 74,088 (h) 1,17,649 (i) 18,15,848
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4. The volume of a cubical tank is 21,97,000 m . Find the length of its side.
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5. The volume of a cubical box is 24,60,375 cm . Find the length of its side.
6. Find the cube roots of the following using the units digit method:
(a) 3,14,432 (b) 8,57,375 (c) 6,36,056
(d) 2,05,379 (e) –3,43,00

Cube Root of a Negative Integral Perfect Cube
The cube root of a negative perfect cube is negative of the cube root of its absolute value.
For any negative integer –a,
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(–a) = (–a) × (–a) × (–a) = –a 3
3
3
3
\ -a 3 = - a 3 fi -a 3 = -a
Example 13: Find the cube root of –17,576 using prime factorization. (NCERT)
Solution: 3 -17 576, = - 17 576,
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Writing 17,576 as a product of its prime factors, we get 2 17,576
17,576 = 2 × 2 × 2 × 13 × 13 × 13 2 8,788
Grouping these into groups of three, we get 2 4,394
17,576 = 2 × 2 × 2 × 13 × 13 × 13 13 2,197

\ 17 576, = 2 ¥¥ 2 13 13 13¥ ¥ ¥ 13 169
2
3
3
13 13
2 13 1
\ 17 576, = 2 × 13 = 26 \ 3 -17 576, = - 17 576, = -26
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3
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