Proved 5-√3 ek aparimey sankhya hai
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let us assume, to the contrary,that(5-√3) is rational.
then, there exist co_primes and b(b not equal to 0)
(5-√3)=a/b
√3=a/b -5
√3= a-5b/b
since a and b are integers,so a-5b/b is rational.
thus ,√3 is also rational.
but , this contradiction the fact that√3 is irrational.so,our assumption is incorrect.
hence ,5-√3 is irrational.
then, there exist co_primes and b(b not equal to 0)
(5-√3)=a/b
√3=a/b -5
√3= a-5b/b
since a and b are integers,so a-5b/b is rational.
thus ,√3 is also rational.
but , this contradiction the fact that√3 is irrational.so,our assumption is incorrect.
hence ,5-√3 is irrational.
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