Cube Root by Prime Factorisation
Cube Root by Prime Factorisation
Procedure:
Step I: Obtain the natural number.
Step II: Express the given natural number as a product of prime factors.
Step III: Group the factors in triples in such a way that all the three factors in each triple are equal.
Step IV: If no factor is left over in grouping in step III, then the number is a perfect cube, otherwise not.
Step V: To find the natural whose cube is the given number, take one factor from each triple and multiply them. The cube of the number so obtained will be the given number.
Illustration 1: What is the smallest number by which 392 must be multiplied so that the product is a perfect cube?
Solution: Resolving 392 into prime factors, we get
Grouping the factors in triplets of equal factors, we get
We find that 2 occurs as a prime factors of 392 thrice but 7 occurs as a prime factor only twice. Thus,if we multiply 392 by 7 ,7 will also occur as a prime factor thrice and the product will which is a perfect cube.
Hence, we must multiply 392 by 7 so that the product becomes a perfect cube.
Illustration 2: What is the smallest number by which 3087 must be divided so that the quotient is a perfect cube?
Solution: Resolving 3087 into prime factors, we get
Grouping the factors in triplets of equal factors, we get
Clearly, if we divided 3087 by , the quotient would be
which is a perfect cube. Therefore, we must divide 3087 by 9 so that the quotient is a perfect cube.
Find the smallest natural number by which 1458 must be divided so that the quotient is a perfect cube. | |||
| Right Option : B | |||
| View Explanation | |||
What is the smallest number by which when 675 is multiplied,the product is a perfect cube? | |||
| Right Option : A | |||
| View Explanation | |||
Write | |||
| Right Option : A | |||
| View Explanation | |||
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Aman Kumar Shrivastava
10thThird consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...
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10thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
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