S.T cube root of 2 is irrational
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Let us assume that √2 is a rational number.
So, 2=a/b(b≠0), where a and b are co-primes.
Taking square on both the sides,
√2²=a²/b²
=2=b²|a²
=2b=a² ------------------(1)
This means 2 divides a² and so 2 divides a.
Let a=c, where c is another integer.
a=2c
Taking square on both sides,
a²=4c² -------------------(2)
from (1) and (2)
2b²=4c²
=b²=4c²/2
=b²=2c²
This means 2 divides b² and so 2 divides b.
This means that a and b have at least 2 and 1 as common factor. Hence, they aren't co-primes. But this contradicts the fact that a and b are co-primes. This contradiction occurred because we assumed √2 as rational. Hence, our assumption is wrong. Therefore, √2 is an irrational number.
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suriya262:
i asked for cube root of 2
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