Question

prove that 3+5√3 is an irrational number​

Answer 1

Answer:

Let 3–5√3 be a rational number and let it be p/q such that p and q are integers and they are not sharing any common factor i. e. they are co-prime integers.

3–5√3 = p/q, therefore ——- I

3–p/q = 5√3, therefore ——- II

(3 - p/q) / 5 = √3 ————— III

The LHS here is a rational number and it is well known that RHS, which is √3 is an irrational number. This is contradictory and since step III is a logical conclusion of step II, which is a logical conclusion of step I, we conclude that step I itself is false and 3–5√3 can’t be a rational number and thus it is proved that 3–5√3 is an irrational number.

Explanation:

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