If someone writes (a=2b) from (a^2=2b^2), what is the correct correction?
Answer and explanation
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.
Frequently asked questions
What is the correct answer to this question?
Since \(a^2\) is even, \(a\) is even; hence write \(a=2k\), where \(k\) is an integer.
Why is this the correct answer?
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.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.
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