Question

prove that 2√3-1is irrational

Answer 1

hey frnd ☺☺

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☆your answeR is given ßelow :--

√3 - √2 is rational .

Let √3 - √2 = r       where r is a rational.

∴  (√3 - √2)2 = r2 

∴  2 + 3 - 2√6 = r2

∴√6 = (5 - r2 ) / 2

Now , LHS = √6 is an irrational number .

RHS =  (5 - r2 ) / 2  But rational number cannot be equal to an irrational.

∴our supposition is wrong.

∴ √3 - √2 is irrational .
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HOPE IT HELPS⤴
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Answer 2

as we know that if we subtract any irrational number with a rational number the result is Ann irrational number so as 2 root 3 is an irrational number and1 is a rational number so 2root 3-1 is an irrational number. hope it helps you