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2) Prove that 3 + 5 is an irrational number. |
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Answer» Answer: Kindly allow me a minute or two ⌚ to check for relevant answers to your question. Please be online. √3 + √5 = a/b On squaring both sides we get, (√3 + √5)² = (a/b)² √3² + √5² + 2(√5)(√3) = a²/b² 3 + 5 + 2√15 = a²/b² 8 + 2√15 = a²/b² 2√15 = a²/b² – 8 √15 = (a²- 8b²)/2b a, b are integers then (a²-8b²)/2b is a RATIONAL number. Then √15 is also a rational number. But this contradicts the fact that √15 is an irrational number. Our assumption is incorrect √3 + √5 is an irrational number. Hence, proved. Step-by-step explanation: hope u have been UNDERSTOOD mark me as BRAINLIST |
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