What is the best exam formula for proving irrationality of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?
Answer and explanation
Correct answer: Take lowest rational form, square, apply prime divisibility, write contradiction with coprimality
Step 1: First assume (\sqrt{r}=\frac{p}{q}) in lowest form. Step 2: Square and use the related prime (r) to show (r\mid p) and (r\mid q). Step 3: Finally write the contradiction with coprimality.
Frequently asked questions
What is the correct answer to this question?
Take lowest rational form, square, apply prime divisibility, write contradiction with coprimality
Why is this the correct answer?
Step 1: First assume (\sqrt{r}=\frac{p}{q}) in lowest form. Step 2: Square and use the related prime (r) to show (r\mid p) and (r\mid q). Step 3: Finally write the contradiction with coprimality.
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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