7.
Prove that (root2 + 1) is an irrational number given that root2 is an irrational number.
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Step-by-step explanation:
Suppose is rational.
Then is rational because rational numbers are closed under addition. Hence, is rational, which is a contradiction. because we know it to be irrational*. Therefore must be irrational.
*Proof that is irrational is left as an exercise for the reader.
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