If someone writes (a=2b) from (a^2=2b^2), what is the correct correction?

Correct answer: Since \(a^2\) is even, \(a\) is even; hence write \(a=2k\), where \(k\) is an integer.

From \(a^2=2b^2\), \(a^2\) is even because it is a multiple of 2. If the square of an integer is even, then the integer itself is even; therefore, write \(a=2k\), where \(k\) is an integer. Writing \(a=2b\) directly is incorrect because \(\sqrt{2b^2}=b\sqrt2\), not \(2b\). Exam tip: In irrationality proofs, first state that an even square implies an even integer.