find √2 is an irrational number?
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It's totally same just replace 5 with 2.
Hope it is helpful to you
Hope it is helpful to you
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Heya!
Here is yr answer......
Let us assume √2 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
by sub. a=2c in eq. a² = 2b²
(2c)² = (2b)²
4c² = 2b²
2c² = b²
b² = 2c²
Since, 2 divides b²
Therefore, 2 also divides b ----------- (2)
From 1 & 2,
we conclude that a, b are not co-primes.
So, our assumption is false.
Therefore, √2 is irrational!
Hope it hlpz...
Here is yr answer......
Let us assume √2 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
by sub. a=2c in eq. a² = 2b²
(2c)² = (2b)²
4c² = 2b²
2c² = b²
b² = 2c²
Since, 2 divides b²
Therefore, 2 also divides b ----------- (2)
From 1 & 2,
we conclude that a, b are not co-primes.
So, our assumption is false.
Therefore, √2 is irrational!
Hope it hlpz...
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