Which statement deeply explains the role of squaring in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?
Answer and explanation
Correct answer: Squaring removes the radical and makes reasoning about prime factor divisibility possible
Step 1: Squaring (\sqrt{n}) gives (n). Step 2: This forms an equation like (p^2=nq^2), which provides the base for divisibility. Step 3: Without this step, it is hard to create the common-factor contradiction.
Frequently asked questions
What is the correct answer to this question?
Squaring removes the radical and makes reasoning about prime factor divisibility possible
Why is this the correct answer?
Step 1: Squaring (\sqrt{n}) gives (n). Step 2: This forms an equation like (p^2=nq^2), which provides the base for divisibility. Step 3: Without this step, it is hard to create the common-factor contradiction.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Proof of irrationality of √2, √3, √5.
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