Page 66 - Maths Skills - 8

64 Maths

Example 3: What is the least number that 576 must be multiplied to make it a perfect cube? 2 576

Solution: First of all, factorising 576 into its prime factors, we get 2 288
576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 2 144
Making it into groups of triple identical factors, we notice that it must be multiplied 2 72
by 3. 2 36
Hence, 576 should be multiplied by the least number, i.e., 3 to make it a perfect cube. 2 18
3 9
Example 4: Find the cube of: 3 3

2
(i) (–8) (i) 2 (iii) 0.05 (iv) 1.4 1
3

8
Solution: (i) (–8) = (–8) × (–8)× (–8) = –512 (i) 2 2 3 8 3 8 8 512
3

3 3 3 3 27
3
(iii) (0.05) = 0.05 × 0.05 × 0.05 = 0.000125 (iv) (1.4) = (1.4) × (1.4) × (1.4) = 2.744
3
3
Exercise 4.1

1. Find out the cubes of the following numbers.
− 4 5
(i) 0.8 (ii) 2.5 (iii) (iv)
7 6
(v) – 5 (vi) 2 3 (vii) 3 (viii) − 13
5 4 15
2. Using prime factorisation method, find which of the following are perfect cubes.
(i) 864 (ii) 1728 (iii) 980 (iv) 729

(v) 2197 (vi) 6750 (vii) 4913 (viii) 5400
3. Find the volume of the cubes, whose each side measures

(i) 7 cm (ii) 4.5 dm (iii) 30 mm (iv) 15.6 cm
4. Find the smallest number by which the following numbers must be divided to make the quotients
perfect cubes.
(i) 54 (ii) 81 (iii) 128 (iv) 2916
5. Find the smallest number by which the following numbers must be multiplied to make them
perfect cubes.

(i) 9 (ii) 72 (iii) 576 (iv) 36

PATTERNS IN CUBES

The cubes of natural numbers can be expressed as sum of consecutive odd numbers as shown below:
 1 = 1 = 1  1 = 1
3
3
2 = 8 = 3 +5 1 + 2 = (1 + 2) 2
3
3
3
3 = 27 = 7 + 9 + 11 1 + 2 + 3 = (1 + 2 + 3) 2
3
3
3
3
4 = 64 = 13 + 15 + 17 + 19 1 + 2 + 3 + 4 = (1 + 2 + 3 + 4) 2
3
3
3
3
3
5 = 125 = 21 + 23 + 25 + 27 + 29
3