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.
By what smallest number must 1080 be divided in order to make it a perfect cube? | |||
| Right Option : B | |||
| View Explanation | |||
Which of the following numbers are the cube of rational numbers? | |||
| Right Option : D | |||
| View Explanation | |||
The smallest number by which 392 must be multiplied so that the product is a perfect cube, is ____________ . | |||
| Right Option : C | |||
| View Explanation |
Students / Parents Reviews [10]
It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
10thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
Barkha Arora
10thAbout 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.
Shreya Shrivastava
8thMy 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.
Ayan Ghosh
8thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
Yatharthi Sharma
10thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
8thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thAbhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
