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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.
Reason : Sum of two irrational numbers is always an irrational number.
- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
DIRECTION : In the following questions, a statement of assertion (A) ...
Here, 2 + √3 + 4 + √3 = 6 + 2√3 which is an irrational number.
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So, Assertion is correct.
Now, 2 + √3 and 4 – √3 are two irrational numbers Sum = 2 + √3 + 4 – √3 = 6 which is a rational number.
So, Reason is not correct.
Correct option is (c) Assertion (A) is true but reason (R) is false.
Most Upvoted Answer
DIRECTION : In the following questions, a statement of assertion (A) ...
Assertion and Reasoning
Assertion: The sum of two irrational numbers 2√3 and 4√3 is an irrational number.
Reasoning: The sum of two irrational numbers is always an irrational number.
Explanation
Irrational Numbers
Irrational numbers are the numbers that cannot be expressed as a ratio of two integers. They are non-repeating and non-terminating decimal numbers. Examples of irrational numbers include √2, √3, and π.
Sum of Two Irrational Numbers
When two irrational numbers are added, the result may or may not be an irrational number. For example, √2 and -√2 are both irrational numbers, but their sum is 0, which is a rational number.
Assertion (A) is True
The sum of two irrational numbers 2√3 and 4√3 is:
2√3 + 4√3 = (2+4)√3 = 6√3
Since √3 is an irrational number and 6 is a rational number, the sum 6√3 is an irrational number.
Reasoning (R) is False
The reasoning that the sum of two irrational numbers is always an irrational number is false. A counterexample to this reasoning is the sum of √2 and -√2, which is 0, a rational number. Therefore, Reasoning (R) is false.
Conclusion
In conclusion, Assertion (A) is true, and Reasoning (R) is false. The sum of two irrational numbers may or may not be an irrational number, depending on the numbers being added.
Assertion: The sum of two irrational numbers 2√3 and 4√3 is an irrational number.
Reasoning: The sum of two irrational numbers is always an irrational number.
Explanation
Irrational Numbers
Irrational numbers are the numbers that cannot be expressed as a ratio of two integers. They are non-repeating and non-terminating decimal numbers. Examples of irrational numbers include √2, √3, and π.
Sum of Two Irrational Numbers
When two irrational numbers are added, the result may or may not be an irrational number. For example, √2 and -√2 are both irrational numbers, but their sum is 0, which is a rational number.
Assertion (A) is True
The sum of two irrational numbers 2√3 and 4√3 is:
2√3 + 4√3 = (2+4)√3 = 6√3
Since √3 is an irrational number and 6 is a rational number, the sum 6√3 is an irrational number.
Reasoning (R) is False
The reasoning that the sum of two irrational numbers is always an irrational number is false. A counterexample to this reasoning is the sum of √2 and -√2, which is 0, a rational number. Therefore, Reasoning (R) is false.
Conclusion
In conclusion, Assertion (A) is true, and Reasoning (R) is false. The sum of two irrational numbers may or may not be an irrational number, depending on the numbers being added.
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.Reason : Sum of two irrational numbers is always an irrational number.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer?
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.Reason : Sum of two irrational numbers is always an irrational number.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. 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 DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.Reason : Sum of two irrational numbers is always an irrational number.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. 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 DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.Reason : Sum of two irrational numbers is always an irrational number.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer?.
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.Reason : Sum of two irrational numbers is always an irrational number.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. 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 DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.Reason : Sum of two irrational numbers is always an irrational number.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. 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 DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.Reason : Sum of two irrational numbers is always an irrational number.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer?.
Solutions for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.Reason : Sum of two irrational numbers is always an irrational number.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.Reason : Sum of two irrational numbers is always an irrational number.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.Reason : Sum of two irrational numbers is always an irrational number.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.Reason : Sum of two irrational numbers is always an irrational number.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.Reason : Sum of two irrational numbers is always an irrational number.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 9 tests.
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