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.
The smallest number by which 8,788 must be divided so that the quotient is perfect cube is : | |||
| Right Option : A | |||
| View Explanation | |||
The value of | |||
| 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 [20]
Abhyas 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...
Aman Kumar Shrivastava
10thBeing 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
8thMy experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thAbout 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
8thWe started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.
Manya
8thMy experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
Hiya Gupta
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
7thMy experience with Abhyas Academy has been very good. When I was not in Abhyas whenever teacher ask questions I could not speak it confidently but when I came in Abhyas, my speaking skills developed and now I am the first one to give the answer of teachers question.
Upmanyu Sharma
7thAbhyas is an institute of high repute. Yogansh has taken admission last year. It creates abilities in child to prepare for competitive exams. Students are motivated by living prizes on basis of performance in Abhyas exams. He is satisfied with institute.
Yogansh Nyasi
7thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
Aman Kumar Shrivastava
10thThe experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confidence to overcome competitive exams. One of the best institutes for secondary education.
Aman Kumar Shrivastava
10thAbhyas 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
10thIt 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
10thMy 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
8thAbhyas 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.
Om Umang
10thI 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
10thAbhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.
Barkha Arora
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 ...
Ayan Ghosh
8thMy experience with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should join Abhyas Academy in tenth class as I am seeing much improvement in Maths and English
Hridey Preet
9thIt 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.
