Page 36 - SM inner class 8.cdr

E xercise 4.1

1. Evaluate the cube of a number.
3 3
5 æ ö æ - ö 2
(i) ( )8 3 (ii) ( )15 3 (iii) ç ÷ (iv) ç ÷
8 è ø è 9 ø

2. Show that 729 is a perfect cube.
3. What is the small est number by which 1323 may be multi plied so that the prod uct is a perfect cube?
4. What is the small est number by which 1375 should be divided so that the quotient may be a perfect
cube?
5. Which of the follow ing are the cubes of even and odd numbers?
(i) 343 (ii) 2744 (iii) 512 (iv) 729
(v) 4096
6. Which of the follow ing are the cubes of odd numbers?
(i) 12167 (ii) 1728 (iii) 3375 (iv) 729
(v) 15625
Cube Root

3
If n = a then we say that ‘a’ is a cube root of n. 19 361
If n is a perfect cube, then its cube root is 19 19
denoted by 3 n. We have observed that in the 1
prime factorisation of a perfect cube, primes
occur in triples. We can therefore find the cube 438976 = 2 3 ´ 2 3 ´19 3
root of a perfect cube ‘n’ as follows : \ 3 438976 = 2 ´ 2 19 = 76
´
1. Find the prime factorization of ‘n’. (ii) We have 250047

2. Group the prime factors into triples of the We find prime factorization by short
same prime. division as follows:

3. Choose one factor from each group and
take their product. The product is the 3 250047
cube root of ‘n’. 3 83349

Example 5. Find the cube root of (i) 438976 (ii) 3 27783
250047
3 9261
Solution:
3 3087
(i) We find the prime factorization by short
division as follows : 3 1029

7 343
2 438976
7 49
2 219488
7 7
2 109744
1
2 54872
3
3
2 27436 250047 = 3 ´ 3 ´ 7 3
3
250047 = 3 ´ 3 ´ 7 = 63
2 13718
19 6859
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Mathematics In Focus - 8