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Question
Is 68600 a perfect cube? If not, find the smallest number by which 68600 must be multiplied to get a perfect cube.
1104 Attempted students
Solution: LCM(68600)=2*2*2*5*5*7*7*7
No, it is not a perfect cube
after multiplying by 5 this number
can be a perfect cube.
150
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We have, 68600 = 2 × 2 × 2 × 5 × 5 × 7 × 7 × 7.
In this factorisation, we find that there is no triplet of 5.
So, 68600 is not a perfect cube.
To make it a perfect cube we multiply it by 5.
Thus,
68600 × 5 = 2 × 2 × 2 × 5 × 5 × 5 × 7 × 7 × 7
= 343000, which is a perfect cube.
- Chapter 7 Class 8 Cubes and Cube Roots
- Serial order wise
- Examples
Check sibling questions
Example 5 - Chapter 7 Class 8 Cubes and Cube Roots
Last updated at Sept. 11, 2018 by
Transcript
Example 5 Is 68600 a perfect cube? If not, find the smallest number by which 68600 must be multiplied to get a perfect cube. We see that 68600 = 2 × 2 × 2 × 5 × 5 × 7 × 7 × 7 Since 5 does not occur in triplets, ∴ 68600 is not a perfect cube. So, we multiply by 5 to make triplet So, our number becomes 68600 × 5 = 2 × 2 × 2 × 5 × 5 × 7 × 7 × 7 × 5 = 2 × 2 × 2 × 5 × 5 × 5 × 7 × 7 × 7 Now, it becomes a perfect cube. So, we multiply 68600 by 5 to make it a perfect cube
- Chapter 7 Class 8 Cubes and Cube Roots
- Serial order wise
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.