Hint for Section 3.7 Question 1b

1b) True. To prove that 1 + sqrt8.jpg (686 bytes)is irrational, you might want to try a proof by contradiction.

Proof Suppose that  1 + sqrt8.jpg (686 bytes) is a rational number. Hence there exist integers a and b such that 1 + sqrt8.jpg (686 bytes)= a / b, where bnoteq.jpg (604 bytes)0.

Now manipulate the equation 1 + sqrt8.jpg (686 bytes)= a / b to show that sqrt2.jpg (659 bytes)is a rational number. This will contradict the fact that we know that sqrt2.jpg (659 bytes)is an irrational number.

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