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)
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∛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 3 Taking one factor from each group ∛13824 = 2 x 2 x 2 x 3 ∛13824 = 24 |
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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
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