Prove that √3 + 2 is an irrational number.
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Step-by-step explanation:
Let us assume, to the contrary, that 32 is
rational. Then, there exist co-prime positive integers a and b such that
32=ba
⇒ 2=3ba
⇒ 2 is rational ...[∵3,a and b are integers∴3bais a rational number]
This contradicts the fact that 2 is irrational.
So, our assumption is not correct.
Hence, 32 is an irrational number
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