Page 73 - Maths Skills - 8

Cubes and Cube Roots 71

MIND MAP

Cubes and Cube Roots

Cube Cube Root
“A number which is a product Cube root of any number ‘x’
of three identical numbers is is denoted by x .
3
called cube of that number” i.e. 82=
3
i.e. 5 = 5 × 5 × 5 = 125
3

Cube Perfect Cube Symbol

Cube of any number Perfect cube of any It is represented by ‘ 3 ’.
may be integer or number must be an
fractional integer

Rememberable Points
If p and q any two integers then
1. 3 pq = 3 p × 3 q
Properties
� Cube of an even number is even. 2. 3 p = 3 p
i.e. 2 = 2 × 2 × 2 = 8; 4 = 4 × 4 × 4 = 64 q 3 q
3
3
� Cube of an odd number is odd.
i.e. 3 = 3 × 3 × 3 = 27; 5 = 5 × 5 × 5 = 125
3
3
� If a number ends with the digit
0, 1, 4, 5, 6, 9 then its cube also ends with the digits 0, 1, 4, 5, 6, 9.
� Cube of any negative number will be always negative
i.e. (–7) = (–7) × (–7) × (–7) = –343
3
� If a number has 3 in its ones place then its cube has 7 in its ones place and vice-versa
i.e. (3) = 3 × 3 × 3 = 27
3
(13) = 13 × 13 × 13 = 2197
3
(7) = 7 × 7 × 7 = 343
3
� If a number has 2 in its ones place then its cube has 8 in its ones place and vice-versa
i.e. (2) = 2 × 2 × 2 = 8
3
(8) = 8 × 8 × 8 = 512
3