CUBES AND CUBE ROOTS

Manpreet Singh

VIII-J

1 23 4

5 67 8

Cubes

Cube Root Vocabulary

index

radicand

radical sign

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.

What does cube root mean?

The cube root of a number is…….

…. the value when multiplied by itself three times gives the original number.

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

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

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

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.

2

2

2

2 x 2 x 2 = 8

3 x 3 x 3 = 27

3

3

3

Examples:

34 4 4 4 64

4643

because

644444 3

because

3 64 4

Examples:

3327

3

5

4

125

64

36216

3273

5

4

125

643

62163

Examples:

33 28 aa

3515 464 yy

3412 327 mm

aa 283 3

53 15 464 yy

43 12 327 mm

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

Thank Youfor

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Submitted by :- Manpreet Singh