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.
To collect rain water, Mini made a cubical tank which can hold | |||
| Right Option : C | |||
| View Explanation | |||
The smallest number by which 2560 must be multiplied so that the product is a perfect cube is : | |||
| Right Option : B | |||
| View Explanation | |||
Which is the least number which when multiplied by 392, the product is the complete cube ? | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [10]
My experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
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Barkha Arora
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Manish Kumar
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Eshan Arora
8thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
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Om Umang
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