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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 : √5 is an irrational number.
Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.
- 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 'A'. Can you explain this answer?
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Verified Answer
DIRECTION : In the following questions, a statement of assertion (A) ...
We know that “A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.” So, Reason is correct.
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Since, √5 cannot be written in the form of p/q, therefore it is an irrational number. Hence assertion is correct follows from reason.
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
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DIRECTION : In the following questions, a statement of assertion (A) ...
Assertion and Reasoning
• Assertion: √5 is an irrational number.
• Reason: A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.
Explanation
• An irrational number is a number that cannot be expressed as the ratio of two integers.
• The square root of 5 is an irrational number because it cannot be expressed as the ratio of two integers.
• Suppose √5 can be expressed as the ratio of two integers p and q, where q ≠ 0.
• Then, we can write √5 = p/q.
• Squaring both sides, we get 5 = p^2/q^2.
• Multiplying both sides by q^2, we get 5q^2 = p^2.
• This means that p^2 is divisible by 5.
• Therefore, p must be a multiple of 5.
• Let p = 5k, where k is an integer.
• Substituting this in √5 = p/q, we get √5 = 5k/q.
• Squaring both sides, we get 5 = 25k^2/q^2.
• Multiplying both sides by q^2, we get 5q^2 = 25k^2.
• This means that q^2 is divisible by 5.
• Therefore, q must be a multiple of 5.
• But this contradicts our assumption that p and q have no common factors.
• Hence, √5 cannot be expressed as the ratio of two integers.
• Thus, the reason given for the assertion is correct.
Conclusion
Both the assertion and the reason are true, and the reason correctly explains the assertion. Hence, the correct answer is option A.
• Assertion: √5 is an irrational number.
• Reason: A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.
Explanation
• An irrational number is a number that cannot be expressed as the ratio of two integers.
• The square root of 5 is an irrational number because it cannot be expressed as the ratio of two integers.
• Suppose √5 can be expressed as the ratio of two integers p and q, where q ≠ 0.
• Then, we can write √5 = p/q.
• Squaring both sides, we get 5 = p^2/q^2.
• Multiplying both sides by q^2, we get 5q^2 = p^2.
• This means that p^2 is divisible by 5.
• Therefore, p must be a multiple of 5.
• Let p = 5k, where k is an integer.
• Substituting this in √5 = p/q, we get √5 = 5k/q.
• Squaring both sides, we get 5 = 25k^2/q^2.
• Multiplying both sides by q^2, we get 5q^2 = 25k^2.
• This means that q^2 is divisible by 5.
• Therefore, q must be a multiple of 5.
• But this contradicts our assumption that p and q have no common factors.
• Hence, √5 cannot be expressed as the ratio of two integers.
• Thus, the reason given for the assertion is correct.
Conclusion
Both the assertion and the reason are true, and the reason correctly explains the assertion. Hence, the correct answer is option A.
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Community Answer
DIRECTION : In the following questions, a statement of assertion (A) ...
We know that the number which is not in the form of of P/Q and non-terminating non-reccuring number is irrational number and the second thing is that all the non perfect square root number is always irrational
FOR-EX---- root 5 , root 6 etccc
FOR-EX---- root 5 , root 6 etccc
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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 : √5 is an irrational number.Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.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 'A'. 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 : √5 is an irrational number.Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.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 '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 DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : √5 is an irrational number.Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.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 '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 DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : √5 is an irrational number.Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.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 'A'. 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 : √5 is an irrational number.Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.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 '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 DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : √5 is an irrational number.Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.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 '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 DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : √5 is an irrational number.Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.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 'A'. 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 : √5 is an irrational number.Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.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 'A'. 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 : √5 is an irrational number.Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.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 'A'. 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 : √5 is an irrational number.Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.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 'A'. 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 : √5 is an irrational number.Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.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 'A'. Can you explain this answer? theory, EduRev gives you an
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