Page 67 - Maths Skills - 8

Cubes and Cube Roots 65

 2 - 1 = 1 + 2 × 1 × 3
3
3
3 - 2 = 1 + 3 × 2 × 3
3
3
4 - 3 = 1 + 4 × 3 × 3
3
3
5 - 4 = 1 + 5 × 4 × 3
3
3
6 - 5 = 1 + 6 × 5 × 3
3
3
CUBE ROOT OF A NUMBER
A number x is the cube root of a number y if y = x .The cube root of a number x is y denoted by x . It can also
3
3
be represented as ()x .
1
3
For example, 2 =8 Index ← 3
3
x → radicand
⇒ 8 = 2
3
Similarly, (– 6) = – 216
3

3
⇒ - 216 = – 6.
Finding Cube Root of a Given Number by Prime Factorisation
We can easily find the cube root of a number by prime factorisation method by following these steps:
Step 1: Write the prime factors of given number. 2 2744

Step 2: Make groups of triplets of identical factors. 2 1372
Step 3: Choose one factor from each triplet and write the product. 2 686
7 343
This product is the required cube root of the given number. 7 49

For example, let us find the value of 2744 . 7 7
3
Fact-o-meter 1
2744 = 2 × 2 × 2 × 7 × 7× 7
3 2744 = 2 × 7 Each prime factor
appears three times in
= 14 its cubes.

⇒ 3 2744 = 14
CUBE ROOT OF A NEGATIVE PERFECT CUBE

If ‘m’ is a positive integer, then the additive inverse of m is – m, which is a negative integer. Also, (– m) = –m 3
3
⇒ - m = (−m ) = – m
3
3
3
3
For example, = - 729 = ( 9 = – 9
3
-
3
3
)
CUBE ROOT OF A RATIONAL NUMBER
p p 3 p
If q be a rational number, then 3 q = 3 q Fact-o-meter
Cube of a number ending
216 3 216
For example, 3 = in 0, 1, 4, 5, 6, 9 ends in 0,
512 3 512
1, 4, 5, 6, 9 respectively in
××
3 666 6 2, 3, 7, 8 ends in 8, 7, 3, 2
= = .
3 ×× respectively and vice versa.
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