Answer :

Assume that 2√3 - 1 is rational

2√3 = a/b , where a and b are integers .

⇒ 2√3 = a/b + 1

⇒ 2√3 = a/b + b/b

⇒ √3 = (a + b) / 2b

we know that a, b, and 2 are integers and they are also rational {i.e RHS is rational}

therefore √3 will be rational.

but we know that √3 is irrational.

there is a contradiction

so, 2√3 - 1 is an irrational number.

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