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Note on Cube Root

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symbol for cube root
Symbol for cube root

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

example for cube root division
Example for cube root division
  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%
  • Find the cube of:

    20

    8000
    2000
    9000
    8500
  • Find the cube of:

    400

     

    64000000
    63000000
    72000000
    6400000
  • Find the cube root of:

    125

     

    5
    2
    1
    7
  • Find the cube root of:

     512

     

    10
    8
    5
    9
  • Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

    243

     

    9
    8
    6
    3
  • Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

     256

     

    7
    3
    5
    2
  • Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

    72

     

    10
    11
    2
    5
  • Find the smallest numbers by which each of the following numbers must be divided to obtain a perfect cube.

    81

    4
     3
    6
    5
  • Find the smallest numbers by which each of the following numbers must be divided to obtain a perfect cube.

    128

     

    4
    2
    7
    8
  • Find the smallest numbers by which each of the following numbers must be divided to obtain a perfect cube.

    135

     

    8
    5
    16
    12
  • Find the smallest numbers by which each of the following numbers must be divided to obtain a perfect cube.

     192

     

    4
    3
    6
    8
  • Find the cube of:

    (-70 ) 

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

    0.06

    (frac{28}{125100})
    (frac{25}{124000})
    (frac{27}{125000})
    (frac{27}{126000})
  • Find the cube root of 5.832.

    1.8
    2.8
    3.9
    1.9
  • Find the cube root of:

    10648

    44
    22
    11
    33
  • You scored /15


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