Which option shows the common deeper idea in the proofs of (\sqrt{3}) and (\sqrt{5})?
Answer and explanation
Correct answer: In a square, the exponent of a prime factor is even, but (p^2=3q^2) or (p^2=5q^2) creates imbalance
Step 1: In a perfect square, exponents of prime factors are even. Step 2: (p^2=3q^2) or (p^2=5q^2) forces the same prime factor into both (p) and (q). Step 3: This common factor contradicts the coprime condition.
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What is the correct answer to this question?
In a square, the exponent of a prime factor is even, but (p^2=3q^2) or (p^2=5q^2) creates imbalance
Why is this the correct answer?
Step 1: In a perfect square, exponents of prime factors are even. Step 2: (p^2=3q^2) or (p^2=5q^2) forces the same prime factor into both (p) and (q). Step 3: This common factor contradicts the coprime condition.
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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