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If A is a positive rational number and N is a positive integer greater than 1 prove that A^n is a rational number?
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If A is a positive rational number and N is a positive integer greater...
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If A is a positive rational number and N is a positive integer greater...
Proof:
Assumption: A is a positive rational number and N is a positive integer greater than 1.
Definition: A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
Claim: A^n is a rational number.
Proof:
To prove that A^n is a rational number, we need to show that it can be expressed as the quotient or fraction p/q of two integers, where q is non-zero.
Let A = p/q, where p and q are integers and q is non-zero (as A is a rational number).
Then, A^n = (p/q)^n = p^n/q^n
Since p and q are integers, p^n and q^n are also integers.
Therefore, we have expressed A^n as the quotient or fraction of two integers, where q^n is non-zero.
Hence, A^n is a rational number.
Conclusion:
Therefore, we have proved that if A is a positive rational number and N is a positive integer greater than 1, then A^n is a rational number.
Assumption: A is a positive rational number and N is a positive integer greater than 1.
Definition: A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
Claim: A^n is a rational number.
Proof:
To prove that A^n is a rational number, we need to show that it can be expressed as the quotient or fraction p/q of two integers, where q is non-zero.
Let A = p/q, where p and q are integers and q is non-zero (as A is a rational number).
Then, A^n = (p/q)^n = p^n/q^n
Since p and q are integers, p^n and q^n are also integers.
Therefore, we have expressed A^n as the quotient or fraction of two integers, where q^n is non-zero.
Hence, A^n is a rational number.
Conclusion:
Therefore, we have proved that if A is a positive rational number and N is a positive integer greater than 1, then A^n is a rational number.
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If A is a positive rational number and N is a positive integer greater than 1 prove that A^n is a rational number?
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If A is a positive rational number and N is a positive integer greater than 1 prove that A^n is a rational number? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If A is a positive rational number and N is a positive integer greater than 1 prove that A^n is a rational number? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A is a positive rational number and N is a positive integer greater than 1 prove that A^n is a rational number?.
If A is a positive rational number and N is a positive integer greater than 1 prove that A^n is a rational number? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If A is a positive rational number and N is a positive integer greater than 1 prove that A^n is a rational number? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A is a positive rational number and N is a positive integer greater than 1 prove that A^n is a rational number?.
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