Take Class 8 Tuition from the Best Tutors
Affordable fees 1-1 or Group class Flexible Timings Verified Tutors Search in
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.
(i) 243
(ii) 256
(iii) 72
(iv) 675
(v) 100
Asked by Manasa Last Modified
Answer (i) 243 = 3 × 3 × 3 × 3 × 3
Here, two 3s are left which are not in a triplet. To make 243 a cube, one more 3 is required.
In that case, 243 × 3 = 3 × 3 × 3 × 3 × 3 × 3 = 729 is a perfect cube.
Hence, the smallest natural number by which 243 should be multiplied to make it a perfect cube is 3.
(ii) 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Here, two 2s are left which are not in a triplet. To make 256 a cube, one more 2 is required.
Then, we obtain
256 × 2 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 512 is a perfect cube.
Hence, the smallest natural number by which 256 should be multiplied to make it a perfect cube is 2.
(iii) 72 = 2 × 2 × 2 × 3 × 3
Here, two 3s are left which are not in a triplet. To make 72 a cube, one more 3 is required.
Then, we obtain
72 × 3 = 2 × 2 × 2 × 3 × 3 × 3 = 216 is a perfect cube.
Hence, the smallest natural number by which 72 should be multiplied to make it a perfect cube is 3.
(iv) 675 = 3 × 3 × 3 × 5 × 5
Here, two 5s are left which are not in a triplet. To make 675 a cube, one more 5 is required.
Then, we obtain
675 × 5 = 3 × 3 × 3 × 5 × 5 × 5 = 3375 is a perfect cube.
Hence, the smallest natural number by which 675 should be multiplied to make it a perfect cube is 5.
(v) 100 = 2 × 2 × 5 × 5
Here, two 2s and two 5s are left which are not in a triplet. To make 100 a cube, we require one more 2 and one more 5.
Then, we obtain
100 × 2 × 5 = 2 × 2 × 2 × 5 × 5 × 5 = 1000 is a perfect cube
Hence, the smallest natural number by which 100 should be multiplied to make it a perfect cube is 2 × 5 = 10.
read lessNow ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com
Ask a QuestionRecommended Articles
5 Engaging Activities For Children To Get...
Learning for every child starts from a very young age. While the formal methods include school curriculums and private lessons, the informal methods include dancing, music, drawing, and various fun-filling activities. Playing games and practising these types of activities helps the children get out of boredom and...
Read full article >
6 Healthy Habits of School Children
While schools provide formal education to the children, the home is where they start learning about things informally. Parents think that schools will take the initiative to educate their children. Well, this is partially true, as parents also play an essential role in bringing up their child. For the development of particular...
Read full article >
Science, Arts Or Commerce - Which One To Go For?
Once over with the tenth board exams, a heavy percentage of students remain confused between the three academic streams they have to choose from - science, arts or commerce. Some are confident enough to take a call on this much in advance. But there is no worry if as a student you take time to make choice between - science,...
Read full article >
Top Benefits of e-Learning
With the current trend of the world going digital, electronic renaissance is a new movement that is welcomed by the new generation as it helps makes the lives of millions of people easier and convenient. Along with this rapidly changing movement and gaining popularity of Internet, e-Learning is a new tool that emerging...
Read full article >
Looking for Class 8 Tuition ?
Learn from the Best Tutors on UrbanPro
Are you a Tutor or Training Institute?
Join UrbanPro Today to find students near youThe best tutors for Class 8 Tuition Classes are on UrbanPro
The best Tutors for Class 8 Tuition Classes are on UrbanPro
