LR Exam > LR Questions > Cube of a natural number will never end with ...
Start Learning for Free
Cube of a natural number will never end with the digit
- a)0
- b)1
- c)3
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Cube of a natural number will never end with the digita)0b)1c)3d)none ...
There'd no such digit which can't end in a cube of a natural number. Hence a cube of a natural number can end with any digit.
1³= 1 (ends with 1)
2³= 8 (ends with 8)
3³= 27 (ends with 7)
4³= 64 (ends with 4)
5³= 125 (ends with 5)
6³= 216 (ends with 6)
7³= 343 (ends with 3)
8³= 512 (ends with 2)
9³= 729 (ends with 9)
0³= 0 (ends with 0)
Hence the last digits are 0,1,8,7,4,5,6,3,2,9
Therefore we see every digits are last digits of these cubes. Hence a cube of a natural number can end with any digit.
1³= 1 (ends with 1)
2³= 8 (ends with 8)
3³= 27 (ends with 7)
4³= 64 (ends with 4)
5³= 125 (ends with 5)
6³= 216 (ends with 6)
7³= 343 (ends with 3)
8³= 512 (ends with 2)
9³= 729 (ends with 9)
0³= 0 (ends with 0)
Hence the last digits are 0,1,8,7,4,5,6,3,2,9
Therefore we see every digits are last digits of these cubes. Hence a cube of a natural number can end with any digit.
Free Test
FREE
| Start Free Test |
Community Answer
Cube of a natural number will never end with the digita)0b)1c)3d)none ...
Explanation:
To understand why the cube of a natural number will never end with the digits 0, 1, or 3, we need to examine the properties of cubes.
Properties of cubes:
1. The cube of any natural number is always a natural number.
2. The unit digit of a perfect cube is determined by the unit digit of the original number.
Unit digit of perfect cubes:
1. If the unit digit of the original number is 0, then the unit digit of its cube will also be 0.
2. If the unit digit of the original number is 1, then the unit digit of its cube will also be 1.
3. If the unit digit of the original number is 2, then the unit digit of its cube will be 8.
4. If the unit digit of the original number is 3, then the unit digit of its cube will be 7.
5. If the unit digit of the original number is 4, then the unit digit of its cube will be 4.
6. If the unit digit of the original number is 5, then the unit digit of its cube will be 5.
7. If the unit digit of the original number is 6, then the unit digit of its cube will be 6.
8. If the unit digit of the original number is 7, then the unit digit of its cube will be 3.
9. If the unit digit of the original number is 8, then the unit digit of its cube will be 2.
10. If the unit digit of the original number is 9, then the unit digit of its cube will be 9.
Explanation of the options:
a) The cube of a natural number can end with 0. For example, the cube of 10 is 1000.
b) The cube of a natural number can end with 1. For example, the cube of 4 is 64.
c) The cube of a natural number can end with 3. For example, the cube of 7 is 343.
Therefore, none of the options (a), (b), or (c) is correct. The cube of a natural number can end with any digit from 0 to 9, depending on the unit digit of the original number.
To understand why the cube of a natural number will never end with the digits 0, 1, or 3, we need to examine the properties of cubes.
Properties of cubes:
1. The cube of any natural number is always a natural number.
2. The unit digit of a perfect cube is determined by the unit digit of the original number.
Unit digit of perfect cubes:
1. If the unit digit of the original number is 0, then the unit digit of its cube will also be 0.
2. If the unit digit of the original number is 1, then the unit digit of its cube will also be 1.
3. If the unit digit of the original number is 2, then the unit digit of its cube will be 8.
4. If the unit digit of the original number is 3, then the unit digit of its cube will be 7.
5. If the unit digit of the original number is 4, then the unit digit of its cube will be 4.
6. If the unit digit of the original number is 5, then the unit digit of its cube will be 5.
7. If the unit digit of the original number is 6, then the unit digit of its cube will be 6.
8. If the unit digit of the original number is 7, then the unit digit of its cube will be 3.
9. If the unit digit of the original number is 8, then the unit digit of its cube will be 2.
10. If the unit digit of the original number is 9, then the unit digit of its cube will be 9.
Explanation of the options:
a) The cube of a natural number can end with 0. For example, the cube of 10 is 1000.
b) The cube of a natural number can end with 1. For example, the cube of 4 is 64.
c) The cube of a natural number can end with 3. For example, the cube of 7 is 343.
Therefore, none of the options (a), (b), or (c) is correct. The cube of a natural number can end with any digit from 0 to 9, depending on the unit digit of the original number.
|
Explore Courses for LR exam
|
|
Similar LR Doubts
Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer?
Question Description
Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer? for LR 2025 is part of LR preparation. The Question and answers have been prepared according to the LR exam syllabus. Information about Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for LR 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer?.
Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer? for LR 2025 is part of LR preparation. The Question and answers have been prepared according to the LR exam syllabus. Information about Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for LR 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for LR.
Download more important topics, notes, lectures and mock test series for LR Exam by signing up for free.
Here you can find the meaning of Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Cube of a natural number will never end with the digita)0b)1c)3d)none of theseCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice LR tests.
|
|
Explore Courses for LR exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup