Prove that is an irrational number. √5 - 2

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KnowledgeBoat · Accepted Answer

Let us assume is a rational number. Let Squaring on both sides, we get : Here, x is rational, ∴ x² is rational .........(1) ⇒ 9 - x² is rational So, is rational. is rational But is irrational is irrational i.e., 9 - x² is irrational and so x² is irrational ........(2) From (1), x² is rational, and from (2), x² is irrational ∴ We arrive at a contradiction. So, our assumption that is a rational number is wrong. ∴ is irrational. Hence, proved that is an irrational number.

Mathematics

Prove that is an irrational number. √5 - 2

Rational Irrational Nos

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