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Prove root 5 is irrational number?
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Prove root 5 is irrational number?
Proving Root 5 is Irrational Number
- Definition of Irrational Number
- Assume root 5 is rational
- Squaring both sides
- Deriving a contradiction
- Conclusion
An irrational number is a number that cannot be expressed as a ratio of two integers.
Let's assume that root 5 is a rational number, which means it can be expressed in the form of p/q, where p and q are integers with no common factors and q is not equal to zero.
Squaring both sides of the equation root 5 = p/q, we get:
5 = p^2/q^2
If 5 = p^2/q^2, then p^2 = 5q^2. This means that p^2 is divisible by 5. Therefore, p must be divisible by 5 as well.
Let p = 5k (where k is an integer)
Substituting p = 5k in the equation p^2 = 5q^2, we get:
25k^2 = 5q^2
5k^2 = q^2
This means that q^2 is divisible by 5. Therefore, q must also be divisible by 5.
However, this contradicts our earlier assumption that p and q have no common factors. Therefore, our assumption that root 5 is a rational number is false.
Therefore, we can conclude that root 5 is an irrational number.
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Prove root 5 is irrational number?
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Prove root 5 is irrational number? 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 Prove root 5 is irrational number? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove root 5 is irrational number?.
Prove root 5 is irrational number? 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 Prove root 5 is irrational number? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove root 5 is irrational number?.
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