Class 9 Exam > Class 9 Questions > The product or quotient of a non-zero rationa...
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The product or quotient of a non-zero rational number with an irrational number is:
- a)Rational number
- b)Whole number
- c)Irrational number
- d)Natural number
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The product or quotient of a non-zero rational number with an irration...
let the no. be 2 and√2so product of it is 2√2 I.e a rational no.
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The product or quotient of a non-zero rational number with an irration...
The product or quotient of a non-zero rational number with an irrational number is an irrational number. This can be explained as follows:
Product of a rational number and an irrational number:
Let's consider a rational number p/q, where p and q are integers and q is not equal to 0, and an irrational number r. The product of these two numbers is:
(p/q) x r = (p x r)/q
Since r is irrational, it cannot be expressed as a quotient of two integers. Therefore, the numerator p x r is also irrational. And since q is an integer, the denominator q is rational. So, we have an irrational number divided by a rational number, which results in an irrational number. Hence, the product of a non-zero rational number with an irrational number is an irrational number.
Quotient of a rational number and an irrational number:
Let's consider a rational number p/q, where p and q are integers and q is not equal to 0, and an irrational number r. The quotient of these two numbers is:
(p/q) ÷ r = (p/q) x (1/r)
Since r is irrational, 1/r is also irrational. So, we have a rational number multiplied by an irrational number, which results in an irrational number. Hence, the quotient of a non-zero rational number with an irrational number is an irrational number.
Therefore, we can conclude that the product or quotient of a non-zero rational number with an irrational number is always an irrational number.
Product of a rational number and an irrational number:
Let's consider a rational number p/q, where p and q are integers and q is not equal to 0, and an irrational number r. The product of these two numbers is:
(p/q) x r = (p x r)/q
Since r is irrational, it cannot be expressed as a quotient of two integers. Therefore, the numerator p x r is also irrational. And since q is an integer, the denominator q is rational. So, we have an irrational number divided by a rational number, which results in an irrational number. Hence, the product of a non-zero rational number with an irrational number is an irrational number.
Quotient of a rational number and an irrational number:
Let's consider a rational number p/q, where p and q are integers and q is not equal to 0, and an irrational number r. The quotient of these two numbers is:
(p/q) ÷ r = (p/q) x (1/r)
Since r is irrational, 1/r is also irrational. So, we have a rational number multiplied by an irrational number, which results in an irrational number. Hence, the quotient of a non-zero rational number with an irrational number is an irrational number.
Therefore, we can conclude that the product or quotient of a non-zero rational number with an irrational number is always an irrational number.
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The product or quotient of a non-zero rational number with an irrational number is:a)Rational numberb)Whole numberc)Irrational numberd)Natural numberCorrect answer is option 'C'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The product or quotient of a non-zero rational number with an irrational number is:a)Rational numberb)Whole numberc)Irrational numberd)Natural numberCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product or quotient of a non-zero rational number with an irrational number is:a)Rational numberb)Whole numberc)Irrational numberd)Natural numberCorrect answer is option 'C'. Can you explain this answer?.
The product or quotient of a non-zero rational number with an irrational number is:a)Rational numberb)Whole numberc)Irrational numberd)Natural numberCorrect answer is option 'C'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The product or quotient of a non-zero rational number with an irrational number is:a)Rational numberb)Whole numberc)Irrational numberd)Natural numberCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product or quotient of a non-zero rational number with an irrational number is:a)Rational numberb)Whole numberc)Irrational numberd)Natural numberCorrect answer is option 'C'. Can you explain this answer?.
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