## Note on Cube Root

• Note
• Things to remember
• Exercise
• Quiz

To find cube root, make triple of equal factors. The opposite of cubing a number is called finding the cube root. A cube root is a number, that is multiplied by itself three times in order to create a cubic value. A cube root of a number x is a number, such that a3= x. All real numbers (except zero) have exactly one real cube root.

Cube of 6 = 6³ =216

Cube root of 216 = 6

Examples

• The cube root of 64 is 4 ( because 4x4x4=64)
• The cube root of 125 is 5 ( because 5x5x5=125)
• The cube root of 512 is 8 ( because 8x8x8=512 )

The symbol, $$\sqrt [3]{}$$, means cube root, so $$\sqrt [3]{27}$$ means "cube root of 27" and $$\sqrt[3]{64}$$means "Cube root of 64"

Thus $$\sqrt [3]{27}$$ = $$\sqrt [3]{3^3}$$ = 3 and $$\sqrt[3]{64}$$ = $$\sqrt[3]{4^3}$$ = 4

A natural number is known as a perfect cube or a cube number.

Cube root of a perfect cube can be found by factorization method.

• The number should be the factor of the prime number or should be expressed as the factor of the prime number.
• Make triples of the factor and each triple should be equal.
• Take one factor from each triple.
• The product is the cube root of the given number.

Examples

1. Find the cube root of 2×2×2×3×3×3
= 2 × 3
= 6

2. Find the cube root of 729.
Solution:
$$\sqrt[3]{729}$$
= $$\sqrt[3]{3×3×3×3×3×3}$$
= $$\sqrt[3]{3^3×3^3}$$
= 3×3
= 9

• A cube root is a number, that multiplied by itself three times in order to create a cubic value.
• To find cube root, make triple of equal factors.
• The opposite of cubing a number is called finding the cube root.
.

### Very Short Questions

Solution:

cube of 6

= 63

= 6×6×6

= 216

Solution:

Cube of 16

= 163

=16 ×16 ×16

= 4096

Solution:

cube root of 125

=$$\sqrt[3]{125}$$

=$$\sqrt[3]{5×5×5}$$

=$$\sqrt[3]{5^3}$$

= 5

 5 125 5 25 5

Solution:

Cube of 20

= 203

= 20 × 20 × 20

= 8000

Soln: Cube of 35=(35)3

=35×35×35

=42875

Solution:

Cube of 400

= 4003

= 400×400×400

= 64000000

Solution:

 3 81 3 27 3 9 3

81 = 3×3×3 =33

∴ The required number is 3.

Solution:

 2 128 2 64 2 32 2 16 2 8 2 4 2

128 = 23×23×2

∴The required number is 2.

Solution:

 3 135 3 45 3 15 5

135 = 33× 5

∴The required number is 5.

Solution:

Cube root of 1331

= $$\sqrt{1331}$$

= $$\sqrt[3]{11 ×11 ×11}$$

= 11

 11 1331 11 121 11

Solution:

 3 243 3 81 3 27 3 9 3

243 = 33× 32

∴The required number is 3.

Solution:

 2 192 2 96 2 48 2 24 2 12 2 6 3

192 = 23×23×3

∴The required number is 3.

Solution:

 5 625 5 125 5 25 5

325 = 53×5

∴The required number is 5.

Solution:

 3 675 3 225 3 75 5 25 5

675 = 33×52

∴The required number is 5.

0%

2000
9000
8000
8500

72000000
63000000
6400000
64000000

7
2
5
1

10
5
9
8

3
6
9
8

7
5
2
3

11
2
10
5

4
3
6
5

7
4
2
8

5
16
12
8

4
8
3
6

-243
343
243
-343
• ### Find the cube of:0.06

(frac{25}{124000})
(frac{27}{125000})
(frac{27}{126000})
(frac{28}{125100})

3.9
1.9
1.8
2.8

11
22
33
44