Question

prove 2√5-3 is an irrational number​

Answer 1

let us assume, to the contrary, that 2√5 − 3 is a rational number

∴ 2√5 − 3 = p/q, where p and q are integers and q ≠ 0 ⇒ √5 = p+3q/2q... (1)

Since p and q are integers ∴ p +3a/2q is a rational number

∴ √5 is a rational number which is a contradiction as √5 is an irrational number

Hence our assumption is wrong and hence 2√5 − 3 is an irrational number.

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