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Which one of the following statements is true?
- a)The sum of two irrational numbers may be a rational number or an irrational number
- b)The sum of two irrational numbers is always an integer
- c)The sum of two irrational numbers is always an irrational number
- d)The sum of two irrational numbers is always a rational number
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Which one of the following statements is true?a)The sum of two irratio...
The sum of two irrational numbers may be a rational number or an irrational number
Eg. a = √2 (which is irrational)
b = 2√2(which is irrational)
a + b = √2 + 2√2 = 3√2 ( which is irrational)
and Let a = 1+√2 (which is irrational)
and b= 1- √2 (which is irrational)
Now, a + b = 1+√2 +1- √2
= 2 (which is rational)
Eg. a = √2 (which is irrational)
b = 2√2(which is irrational)
a + b = √2 + 2√2 = 3√2 ( which is irrational)
and Let a = 1+√2 (which is irrational)
and b= 1- √2 (which is irrational)
Now, a + b = 1+√2 +1- √2
= 2 (which is rational)
Most Upvoted Answer
Which one of the following statements is true?a)The sum of two irratio...
The sum of two irrational numbers could be either rational or irrational. We can show this through examples: and are each irrational, but their sum is 0, which is rational. and are each irrational, and their sum is irrational.
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Which one of the following statements is true?a)The sum of two irratio...
Explanation:
Sum of two irrational numbers:
When we add two irrational numbers, the result can be either rational or irrational, depending on the numbers being added.
Example:
Let's consider two irrational numbers √2 and √3.
- The sum of √2 and √3 is irrational: √2 + √3 ≈ 3.146.
- However, the sum of √2 and (-√2) is rational: √2 + (-√2) = 0.
Conclusion:
Therefore, the sum of two irrational numbers may be a rational number or an irrational number, as demonstrated in the examples above. This shows that option 'a' is the correct statement.
Sum of two irrational numbers:
When we add two irrational numbers, the result can be either rational or irrational, depending on the numbers being added.
Example:
Let's consider two irrational numbers √2 and √3.
- The sum of √2 and √3 is irrational: √2 + √3 ≈ 3.146.
- However, the sum of √2 and (-√2) is rational: √2 + (-√2) = 0.
Conclusion:
Therefore, the sum of two irrational numbers may be a rational number or an irrational number, as demonstrated in the examples above. This shows that option 'a' is the correct statement.
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Which one of the following statements is true?a)The sum of two irrational numbers may be a rational number or an irrational numberb)The sum of two irrational numbers is always an integerc)The sum of two irrational numbers is always an irrational numberd)The sum of two irrational numbers is always a rational numberCorrect answer is option 'A'. Can you explain this answer?
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Which one of the following statements is true?a)The sum of two irrational numbers may be a rational number or an irrational numberb)The sum of two irrational numbers is always an integerc)The sum of two irrational numbers is always an irrational numberd)The sum of two irrational numbers is always a rational numberCorrect answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Which one of the following statements is true?a)The sum of two irrational numbers may be a rational number or an irrational numberb)The sum of two irrational numbers is always an integerc)The sum of two irrational numbers is always an irrational numberd)The sum of two irrational numbers is always a rational numberCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following statements is true?a)The sum of two irrational numbers may be a rational number or an irrational numberb)The sum of two irrational numbers is always an integerc)The sum of two irrational numbers is always an irrational numberd)The sum of two irrational numbers is always a rational numberCorrect answer is option 'A'. Can you explain this answer?.
Which one of the following statements is true?a)The sum of two irrational numbers may be a rational number or an irrational numberb)The sum of two irrational numbers is always an integerc)The sum of two irrational numbers is always an irrational numberd)The sum of two irrational numbers is always a rational numberCorrect answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Which one of the following statements is true?a)The sum of two irrational numbers may be a rational number or an irrational numberb)The sum of two irrational numbers is always an integerc)The sum of two irrational numbers is always an irrational numberd)The sum of two irrational numbers is always a rational numberCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following statements is true?a)The sum of two irrational numbers may be a rational number or an irrational numberb)The sum of two irrational numbers is always an integerc)The sum of two irrational numbers is always an irrational numberd)The sum of two irrational numbers is always a rational numberCorrect answer is option 'A'. Can you explain this answer?.
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Which one of the following statements is true?a)The sum of two irrational numbers may be a rational number or an irrational numberb)The sum of two irrational numbers is always an integerc)The sum of two irrational numbers is always an irrational numberd)The sum of two irrational numbers is always a rational numberCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Which one of the following statements is true?a)The sum of two irrational numbers may be a rational number or an irrational numberb)The sum of two irrational numbers is always an integerc)The sum of two irrational numbers is always an irrational numberd)The sum of two irrational numbers is always a rational numberCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Which one of the following statements is true?a)The sum of two irrational numbers may be a rational number or an irrational numberb)The sum of two irrational numbers is always an integerc)The sum of two irrational numbers is always an irrational numberd)The sum of two irrational numbers is always a rational numberCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which one of the following statements is true?a)The sum of two irrational numbers may be a rational number or an irrational numberb)The sum of two irrational numbers is always an integerc)The sum of two irrational numbers is always an irrational numberd)The sum of two irrational numbers is always a rational numberCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 9 tests.
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