Which conclusion is correct for all three numbers (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?
Answer and explanation
Correct answer: All three are irrational numbers
Step 1: (2,3,5) are prime numbers and not perfect squares. Step 2: Assuming their square roots rational creates a common factor in the coprime numerator and denominator. Step 3: Therefore (\sqrt{2}), (\sqrt{3}), and (\sqrt{5}) are all irrational.
Frequently asked questions
What is the correct answer to this question?
All three are irrational numbers
Why is this the correct answer?
Step 1: (2,3,5) are prime numbers and not perfect squares. Step 2: Assuming their square roots rational creates a common factor in the coprime numerator and denominator. Step 3: Therefore (\sqrt{2}), (\sqrt{3}), and (\sqrt{5}) are all irrational.
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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