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Prove that √3 − √2 is an irrational number |
Answer» Let √3 − √2 = r where r be a rational number Squaring both sides ⇒ (√3-√2)2= r2 ⇒ 3 + 2 - 2 √6 = r2 ⇒ 5 - 2 √6 = r2 Here, 5 - 2√6 is an irrational number but r2 is a rational number ∴ L.H.S. ≠ R.H.S. Hence it contradicts our assumption that √3 − √2 is a rational number. |
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