prove that (2 + 2√3)is not a rational number.
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Proof : Let (√2 + 3)/√2 be a rational number which is equal to x. Thus √2 is in p/q form and hence a rational number. This leads to contradiction for a fact that √2 is actually an irational number. That's why (√2 + 3)/√2 is not a rational number
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