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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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.
Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.
- 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) ...
We know that If the product of two irrational numbers is rational then each one is called the rationalising factor of the other. So, Reason is correct.
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Now, (3 + 2√5) x (3 – 2√5) = 32 – (2√5)2
= 9 – 20 = – 11
So, both Assertion and Reason are correct and Reason explains Assertion.
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: The rationalizing factor of 3 2√5 is 3 – 2√5.
Reason: If the product of two irrational numbers is rational then each one is called the rationalizing factor of the other.
Explanation:
- Irrational numbers: Numbers that cannot be expressed as simple fractions and their decimal expansions are non-ending and non-repeating are known as irrational numbers. For example, √2, √3, π, e, etc.
- Rationalizing factor: The process of converting an irrational number into a rational number is known as rationalizing. The factor used to rationalize the irrational number is called the rationalizing factor.
- Product of two irrational numbers: Let a and b be two irrational numbers. If their product, ab, is rational, then each number is called the rationalizing factor of the other.
- Rationalizing a surd: A surd is an irrational number that can be expressed as the root of a non-perfect square. For example, √2, √3, √5, etc. To rationalize a surd, we multiply the numerator and denominator by a suitable rationalizing factor.
Now, let us come to the given assertion and reason:
- Assertion: The rationalizing factor of 3 2√5 is 3 – 2√5.
To rationalize the given surd, we multiply the numerator and denominator by its conjugate. The conjugate of 3 + 2√5 is 3 – 2√5. Therefore,
(3 + 2√5)(3 – 2√5) = 9 – 20 = -11
Hence, the rationalizing factor of 3 2√5 is 3 – 2√5.
- Reason: If the product of two irrational numbers is rational then each one is called the rationalizing factor of the other.
Let a and b be two irrational numbers such that ab is rational. Then, we can express b as b = ab/a. Since a and ab are both irrational, a must be a rationalizing factor of b. Similarly, b is a rationalizing factor of a.
Therefore, the given reason is correct.
- Option (a): Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Hence, option (a) is the correct answer.
Assertion: The rationalizing factor of 3 2√5 is 3 – 2√5.
Reason: If the product of two irrational numbers is rational then each one is called the rationalizing factor of the other.
Explanation:
- Irrational numbers: Numbers that cannot be expressed as simple fractions and their decimal expansions are non-ending and non-repeating are known as irrational numbers. For example, √2, √3, π, e, etc.
- Rationalizing factor: The process of converting an irrational number into a rational number is known as rationalizing. The factor used to rationalize the irrational number is called the rationalizing factor.
- Product of two irrational numbers: Let a and b be two irrational numbers. If their product, ab, is rational, then each number is called the rationalizing factor of the other.
- Rationalizing a surd: A surd is an irrational number that can be expressed as the root of a non-perfect square. For example, √2, √3, √5, etc. To rationalize a surd, we multiply the numerator and denominator by a suitable rationalizing factor.
Now, let us come to the given assertion and reason:
- Assertion: The rationalizing factor of 3 2√5 is 3 – 2√5.
To rationalize the given surd, we multiply the numerator and denominator by its conjugate. The conjugate of 3 + 2√5 is 3 – 2√5. Therefore,
(3 + 2√5)(3 – 2√5) = 9 – 20 = -11
Hence, the rationalizing factor of 3 2√5 is 3 – 2√5.
- Reason: If the product of two irrational numbers is rational then each one is called the rationalizing factor of the other.
Let a and b be two irrational numbers such that ab is rational. Then, we can express b as b = ab/a. Since a and ab are both irrational, a must be a rationalizing factor of b. Similarly, b is a rationalizing factor of a.
Therefore, the given reason is correct.
- Option (a): Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Hence, option (a) is the correct 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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.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
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 : The rationalizing factor of 3 + 2√5 is 3 – 2√5.Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.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? tests, examples and also practice Class 9 tests.
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