prove that root 2 and root 3 is irrational
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it gives in some decimal point
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let√2 be rational
√2=a/b where a and b are co primes
(√2)^2=(a/b)^2
2=a^2/b^2
2b^2=a^2
2 | a^2
2 | a
a=2c for some integer c
a^2=4c^2
2b^2=4c^2
b^2=2c^2
2 | b^2
2 | b
From this we get that 2 is the common factor of a and b. But this contradiction is wrong . Therefore √2 is irrational.
√3 will be in the similar way.
Hope this will help you.
√2=a/b where a and b are co primes
(√2)^2=(a/b)^2
2=a^2/b^2
2b^2=a^2
2 | a^2
2 | a
a=2c for some integer c
a^2=4c^2
2b^2=4c^2
b^2=2c^2
2 | b^2
2 | b
From this we get that 2 is the common factor of a and b. But this contradiction is wrong . Therefore √2 is irrational.
√3 will be in the similar way.
Hope this will help you.
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