Which type of square root is proved irrational in proofs like those for (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?
Answer and explanation
Correct answer: The square root of a prime number that is not a perfect square
Step 1: (2,3,5) are prime numbers and not perfect squares. Step 2: Assuming their square roots rational creates the same prime as a common factor of numerator and denominator. Step 3: Understand the difference between a perfect square and a prime number.
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What is the correct answer to this question?
The square root of a prime number that is not a perfect square
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 the same prime as a common factor of numerator and denominator. Step 3: Understand the difference between a perfect square and a prime number.
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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