Cube Root

Subject: Compulsory Maths

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Overview

To cube a number, just use it in a multiplication 3 times.A cube root is a number that multiplies by itself three times in order to create a cubic value.In some contexts, particularly when the number, one of the cube roots ( in this particular case the real one) is referred to as the principal cube root.

Cube Root
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

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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
Things to remember
  • 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. 
  • It includes every relationship which established among the people.
  • There can be more than one community in a society. Community smaller than society.
  • It is a network of social relationships which cannot see or touched.
  • common interests and common objectives are not necessary for society.
Questions and Answers

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.

Solution:

2 4096
2 2048
2 1024
2 512
2 256
2 128
2 64
2 32
2 16
2 8
2 4
2

= \(\sqrt{2×2×2×2×2×2×2×2×2×2×2×2}\)

= \(\sqrt[3]{2^3×2^3×2^3×2^3}\)

=2 × 2 × 2 × 2

= 16

Solution:

2 2744
2 1372
2 686
7 343
7 49
7

= \(\sqrt[3]{2×2×2×7×7×7}\)

= \(\sqrt[3]{2^3×7^3}\)

= 2 × 7

= 14

∴ The Cube root of 2744 is 14.

Solution:

3 3375
3 1125
3 375
5 125
5 25
5

= \(\sqrt[3]{3×3×3×5×5×5}\)

= \(\sqrt[3]{3^3×5^3}\)

= 3 × 5

= 15

∴ The Cube root of 3375 is 15.

Solution:

2 10648
2 5324
2 2662
11 331
11 121
11

= \(\sqrt[3]{2×2×2×11×11×11}\)

= \(\sqrt[3]{2^3×11^3}\)

= 2 × 11

= 22

∴ Cube root of 10648 is 22.

Solution:

2 216
2 108
2 54
3 27
3 9
3

2 64
2 32
2 16
2 8
2 4
2

\(\sqrt[3]{\frac{2×2×2×3×3×3}{2×2×2×2×2×2}}\)

= \(\sqrt[3]{\frac{3^3}{2^3}}\)

= \(\frac{3}{2}\)

Solution:

2 8
2 4
2

3 27
3 9
3

= \(\sqrt[3]{2×2×2}\) + \(\sqrt[3]{3×3×3}\)

=\(\sqrt[3]{2^3}\) + \(\sqrt[3]{3^3}\)

= 2 + 3

= 5

Solution:

\(\sqrt[3]{3×3×3}\)× \(\sqrt[3]{-3×-3×-3}\)

= \(\sqrt[3]{3^3}\)× \(\sqrt[3]{(-3^3}\))

= 3×(-3)

= -9

Solution:

\(\sqrt[3]{2×2×2}\) + \(\frac{1}{\sqrt[3]{2×2×2}}\)

= \(\sqrt[3]{2^3}\) + \(\frac{1}{\sqrt[3]{2^3}}\)

= 2 + \(\frac{1}{2}\)

= \(\frac{2×2 +1×2}{2}\)

= \(\frac{5}{2}\)

Solution:

= \(\sqrt[3]{3×3×3}\) - \(\frac{1}{\sqrt[3]{3×3×3}}\)

= 3 - \(\frac{1}{3}\)

= \(\frac{3×3-1×1}{3}\)

= \(\frac{9-1}{3}\)

= \(\frac{8}{3}\)

Solution:

Cube root of 400

= (400)3

= 400 × 400 × 400

= 64,000,000

∴ Cube root of 400 is 64,000,000.

Quiz

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