show that root 2 is irrational
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Heya!
Here is yr answer.....
Let us assume √2 is rational!
=> √2 = a/b (a, b are co-primes)
=> b√2 = a
by squaring on both sides.....
=> 2b² = a²
=> a² = 2b²
Here, 2 divides a²
Therefore, 2 also divides a ------(1)
Let a = 2c
=> (2c)² = 2b²
=> 4c² = 2b²
=> 2c² = b²
=> b² = 2c²
Here, 2 divides b²
Therefore, 2 also divides b ----(2)
From (1) & (2)
We can conclude that, a , b are nkt co-primes!
Hence, our assumption is false
Therefore, √2 is irrational!
HENCE PROVED!!
Hope it hlpz..
Here is yr answer.....
Let us assume √2 is rational!
=> √2 = a/b (a, b are co-primes)
=> b√2 = a
by squaring on both sides.....
=> 2b² = a²
=> a² = 2b²
Here, 2 divides a²
Therefore, 2 also divides a ------(1)
Let a = 2c
=> (2c)² = 2b²
=> 4c² = 2b²
=> 2c² = b²
=> b² = 2c²
Here, 2 divides b²
Therefore, 2 also divides b ----(2)
From (1) & (2)
We can conclude that, a , b are nkt co-primes!
Hence, our assumption is false
Therefore, √2 is irrational!
HENCE PROVED!!
Hope it hlpz..
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