Prove that √2 is irrational by contradiction method.
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We will prove whether √2 is irrational by contradiction method.
Let √2 be rational
It can be expressed as √2 = a/b ( where a, b are integers and co-primes.
√2 = a/b
2= a²/b²
2b² = a²
2 divides a²
By the Fundamental theorem of Arithmetic
so, 2 divides a .
a = 2k (for some integer)
a² = 4k²
2b² = 4k²
b² = 2k²
2 divides b²
2 divides b.
Now 2 divides both a & b this contradicts the fact that they are co primes.
this happened due to faulty assumption that √2 is rational. Hence, √2 is irrational.
Read more on Brainly.in - https://brainly.in/question/2646257#readmore
Let √2 be rational
It can be expressed as √2 = a/b ( where a, b are integers and co-primes.
√2 = a/b
2= a²/b²
2b² = a²
2 divides a²
By the Fundamental theorem of Arithmetic
so, 2 divides a .
a = 2k (for some integer)
a² = 4k²
2b² = 4k²
b² = 2k²
2 divides b²
2 divides b.
Now 2 divides both a & b this contradicts the fact that they are co primes.
this happened due to faulty assumption that √2 is rational. Hence, √2 is irrational.
Read more on Brainly.in - https://brainly.in/question/2646257#readmore
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