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1. CUBES AND CUBE
ROOTS
Manpreet Singh
VIII-J

2. 1 2
3 4
5 6
7 8
Cubes

3. Cube Root Vocabulary
index
radicand
radical sign

4. Cube Root
 The cube root of a number is a
special value that, when used
in a multiplication three times,
gives that number.
Example: 3 × 3 × 3 = 27, so
the cube root of 27 is 3.

5. What does cube root mean?
 The cube root of a number is…….
…. the value when multiplied by itself three
times gives the original number.

6. Properties of Cube Roots
 If a and b are any two whole numbers, then 3 a×b =
3 a × 3 b .
 If a and b are any two whole numbers (b = 0), then
3 a/b = 3 a
3
b

7. Properties of Cube of
numbers
 Cube of all even natural are even.
Cube of 4 = 64, which is an even number
 Cube of all odd natural are odd.
Cube of 3 = 27, which is even number
 Cube of a natural number of the form 3n is a multiple of 27.
Cube of 7 = 343, which is of the form 3n+1
 Cube of a natural number of the form 3n+1 is also a number
of the form 3n+1.
Cube of 5 = 125, which is of the form 3n+2

8. You can also cube negative
numbers
 If you cube 5 you get 125: 5 5 5 = 125
 If you cube -5 you get -125: -5 -5 -5 = -125
So the cube root of -125 is -5

9. Method of finding a perfect Cube
 To check weather a given number is a perfect
cube or not
1. Resolve the given number into prime factors.
2. Group together the triples of like prime
factors.
3. If no factor is left ungrouped, the given
number is a perfect cube.

10. 2
2
2
2 x 2 x 2 = 8

11. 3 x 3 x 3 = 27
3
3
3

12. Examples:
     
3
4 4 4 4 64 
4643

because
      644444
3

because
3
64 4  

13. Examples:
3
327 
3
5
4
125
64







3
6216 
3273

5
4
125
643 
62163


14. Examples:
 33
28 aa 
 3515
464 yy 
 3412
327 mm 
aa 283 3

53 15
464 yy 
43 12
327 mm 

15. Not all cube roots
can be simplified!
• 30 is not a perfect cube.
• 30 does not have a perfect cube
factor.
Example: 3
30
cannot be simplified!
3
30

16. Thank You
for
Watching this Presentation
Submitted by :- Manpreet Singh