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# Prove that 3+2√5 is irrational?

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Prove that 3+2√5 is irrational?

Nitika Arya 2 months, 2 weeks ago

￼ ￼ Use app Login Class 10 >>Maths >>Real Numbers >>Revisiting Irrational Numbers >>Prove that 3 + 2√(5) is irrational. Question ￼ Prove that 3+25​ is irrational. Medium Open in App￼ Updated on : 2022-09-05 Solution ￼ Verified by Toppr Prove 3+25​ is irrational. → let take that 3+25​is rational number → so, we can write this answer as ⇒3+25​=ba​  Here a & b use two coprime number and b=0. ⇒25​=ba​−3 ⇒25​=ba−3b​ ∴5​=2ba−3b​ Here a and b are integer so 2ba−3b​ is a rational number so 5​ should be rational number but 5​ is a irrational number so it is contradict - Hence 3+25​ is irrational.

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