Prove that
Is irrational number
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hi mate your question is,
to prove: 5-2√3 is an irrational number.
solution:- let us assume that 5-2√3 is a rational number.
so, 5-2√3 = p/q
-2√3 = p/q - 5
-2√3 = p-5q/ q
√3 = p-5q/2q
but this contradicts the fact that 5-√3 is a rational number. p-5q/2q is a rational number but √3 is an irrational number so they irrational number is not equal to rational number.
therefore, our assumption is wrong
5-2√3 is an irrational number
hence proved
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