# Finding Cube Root by Prime Factorization

In order of finding cube root by prime factorization we use the following steps :**Step I :**Obtain the given number.

**Step II :**Resolve it into prime factors.

**Step III :**Group the factors in 3 in such a way that each number of the group is same.

**Step IV :**Take one factor from each group.

**Step V :**Find the product of the factors obtained in step IV. This product is the required cube root.

**Examples : Finding the cube root by prime factorization**

1) ∛64

**Solution :**

64 = 2 x 32

= 2 x 2 x 16

= 2 x 2 x 2 x 8

= 2 x 2 x 2 x 2 x 4

=

__2 x 2 x 2__x

__2 x 2 x 2__(make the groups of 3 of equal numbers)

There are two groups, so from each group take one factor

∴ ∛64 = 2 x 2

∴

**∛64 = 4**

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2)

∛13824 Solution :After resolving the prime factors, we get 13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 Grouping = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3Taking one factor from each group ∛13824 = 2 x 2 x 2 x 3 ∛13824 = 24 |

**Cube and Cube Roots**

• Cube of Numbers

• Perfect Cube

• Properties of Cube

• Cube by Column method

• Cube of Negative numbers

• Cube of Rational numbers

• Cube Root

• Finding cube root by Prime Factorization

• Cube root of Rational numbers

• Estimating cube root

• Cube of Numbers

• Perfect Cube

• Properties of Cube

• Cube by Column method

• Cube of Negative numbers

• Cube of Rational numbers

• Cube Root

• Finding cube root by Prime Factorization

• Cube root of Rational numbers

• Estimating cube root

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