A natural number is said to be a perfect cube if it is the cube of some natural number.
Example
8 = 2 x 2 x 2
8 = 2 ³
8 is the perfect cube because it is a cube of 2 which is a natural number.
But 12 is not a perfect cube because it is not a cube of any natural numbers.

Question

A natural number is said to be a perfect cube, if it is the cube of some ________.a)cube numberb)square numbersc)natural numberd)none of theseCorrect answer is 'C'. Can you explain this answer?

Answer

Answer

It could also a

Answer

Ans. c

Answer

C is the correct answer because 0 is a cube and square number but it's cube is not a natural number because it will also be 0 so a natural number is a perfect cube only of a natural number

Answer

I could be a also.

Answer

C

Answer

A perfect cube is a number that can be expressed as the cube of a natural number.

To understand the answer, let's break it down into the following headings:

1. Definition of a perfect cube
A perfect cube is a number that is the cube of a natural number. In other words, it is the result of multiplying a natural number by itself twice. For example, 8 is a perfect cube because it can be expressed as 2 × 2 × 2.

2. Cube numbers
A cube number is a number that can be expressed as the cube of an integer. The cube of a number is obtained by multiplying the number by itself twice. For example, 2 × 2 × 2 = 8, so 8 is a cube number.

3. Square numbers
A square number is a number that can be expressed as the square of an integer. The square of a number is obtained by multiplying the number by itself. For example, 2 × 2 = 4, so 4 is a square number. However, not all square numbers are perfect cubes. For example, 4 is a square number but not a perfect cube.

4. Natural numbers
Natural numbers are the counting numbers starting from 1. They include all positive integers, but not zero or negative numbers. For example, 1, 2, 3, 4, 5, etc., are natural numbers.

5. Explanation of the correct answer (Option C)
The correct answer is option C - a natural number. This is because a perfect cube is defined as a number that can be expressed as the cube of a natural number. In other words, if we take the cube root of a perfect cube, the result will be a natural number. For example, the cube root of 8 is 2, which is a natural number.

6. Explanation of incorrect options
- Option A (cube number) is incorrect because not all cube numbers are perfect cubes. Some cube numbers, such as 4, are not perfect cubes.
- Option B (square numbers) is incorrect because not all square numbers are perfect cubes. Some square numbers, such as 4, are not perfect cubes.
- Option D (none of these) is incorrect because the correct answer is option C, as explained above.

In conclusion, a natural number is said to be a perfect cube because it can be expressed as the cube of a natural number. This distinction is important as it differentiates perfect cubes from cube numbers and square numbers.

Similar UPSC Doubts

For any-natural numbers, let K be the index of the highest power of 2 which divides the number. Among the first 100 natural numbers all those. numbers for which K is even, are excluded. Find the index of the highest power of 2 which divides the product of the remaining numbers.?

The number of non - perfect square numbers between the squares of 49 and 50.?

A positive number is 4 times another number. If 16 is added to both the numbers, then one of the new numbers becomes thrice the other new number. What are the numbers?

Q.10. A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11? (

A positive number is 5 times another number. if 21 is added to both the numbers, then one of the new numbers become twice the other new number. what are the numbers?

Top Courses for UPSCView all

Current Affairs & Hindu Analysis: Daily, Weekly & Monthly

Lucent for GK

History for UPSC CSE

Indian Polity for UPSC CSE

CSAT Preparation

Top Courses for UPSC

Top Courses for UPSC

Related Content

About UPSC

UPSC Preparation Material

NCERT Based Study Material

How to Prepare for UPSC Exam?

Famous Books for UPSC Exam

UPSC Subjects

UPSC Optionals

Other Popular Exams

Company