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√5 is irrational Or rational?
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√5 is irrational Or rational?
Is √5 Rational or Irrational?
- Definition: A rational number is a number that can be expressed as a ratio of two integers, while an irrational number cannot.
- Square Root of 5: The square root of 5 (√5) is a number that, when multiplied by itself, equals 5.
- Proof: We can prove that √5 is irrational by contradiction. Assume that √5 is rational, which means that it can be expressed as a ratio of two integers in the lowest terms, i.e., √5 = a/b, where a and b are integers with no common factors.
- Squaring Both Sides: Squaring both sides of the equation gives 5 = a^2/b^2.
- Multiplying: Multiplying both sides by b^2 gives 5b^2 = a^2.
- Conclusion: This means that a^2 is divisible by 5, which implies that a is also divisible by 5. Therefore, we can write a = 5k, where k is an integer.
- Substituting: Substituting a = 5k into the equation 5b^2 = a^2 gives 5b^2 = (5k)^2 = 25k^2.
- Reducing: Dividing both sides by 5 gives b^2 = 5k^2.
- Conclusion: This means that b^2 is divisible by 5, which implies that b is also divisible by 5. However, this contradicts our assumption that a and b have no common factors. Therefore, our initial assumption that √5 is rational is false, and √5 is irrational.
In conclusion, the square root of 5 (√5) is an irrational number.
Community Answer
√5 is irrational Or rational?
It is irrational number because you cannot express it in the form of p/q where p and q are some integers and q doesn't equal to 0.
How you can find that a number is rational or irrational:-
* For rational number:-
_ It will be terminating or non-terminating( Repeating/ Reoccurring)
* For irrational number:-
_ It will be non-terminating(Non- repeating/ Non-reoccuring)
I hope you have understand the concept clearly now.
And don't forget that:- "Concept is Power".
How you can find that a number is rational or irrational:-
* For rational number:-
_ It will be terminating or non-terminating( Repeating/ Reoccurring)
* For irrational number:-
_ It will be non-terminating(Non- repeating/ Non-reoccuring)
I hope you have understand the concept clearly now.
And don't forget that:- "Concept is Power".
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√5 is irrational Or rational?
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√5 is irrational Or rational? 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 √5 is irrational Or rational? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for √5 is irrational Or rational?.
√5 is irrational Or rational? 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 √5 is irrational Or rational? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for √5 is irrational Or rational?.
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