Prove that minus root 2 is an irrational
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√2 = a/b
2 = a2/b2
If we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:
2=(2k)2/b2
2=4k2/b2
2*b2=4k2
b2=2k2
This means that b2 is even, from which follows again that b itself is even.
2 = a2/b2
If we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:
2=(2k)2/b2
2=4k2/b2
2*b2=4k2
b2=2k2
This means that b2 is even, from which follows again that b itself is even.
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Given that √2 is a irrational number
Let us consider a/b is a rational number.
√2=a/b.
Here, a/b is a rational number then √2 is also a rational number, but our assumption is wrong. Hence by contradiction method
√2 is an irrational number.
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