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Prove under root 1÷2 is irrational?
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Prove under root 1÷2 is irrational?
To prove 1/√2 is irrational
Let us assume that √2 is irrational
1/√2 = p/q (where p and q are co prime)
q/p = √2
q = √2p
squaring both sides
q² = 2p² (1)
By theorem
q is divisible by 2
∴ q = 2c ( where c is an integer)
putting the value of q in equitation 1
2p² = q² = 2c² =4c²
p² =4c² /2 = 2c²
p²/2 = c²
by theorem p is also divisible by 2
But p and q are coprime
This is a contradiction which has arisen due to our wrong assumption
∴1/√2 is irrational.
Let us assume that √2 is irrational
1/√2 = p/q (where p and q are co prime)
q/p = √2
q = √2p
squaring both sides
q² = 2p² (1)
By theorem
q is divisible by 2
∴ q = 2c ( where c is an integer)
putting the value of q in equitation 1
2p² = q² = 2c² =4c²
p² =4c² /2 = 2c²
p²/2 = c²
by theorem p is also divisible by 2
But p and q are coprime
This is a contradiction which has arisen due to our wrong assumption
∴1/√2 is irrational.
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Prove under root 1÷2 is irrational?
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Prove under root 1÷2 is irrational? 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 Prove under root 1÷2 is irrational? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove under root 1÷2 is irrational?.
Prove under root 1÷2 is irrational? 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 Prove under root 1÷2 is irrational? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove under root 1÷2 is irrational?.
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