Real Numbers
Himachal Pradesh Board · Class 10 · Mathematics
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What is the Fundamental Theorem of Arithmetic primarily concerned with?
Is √2 a rational or irrational number?
What is the prime factorization of 32760?
What does the Fundamental Theorem of Arithmetic guarantee about prime factorization?
Sample Questions
If p is a prime number and p divides a², what can be concluded about a?
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p must divide a
If a prime p divides a², then p must also divide a, as proven in Theorem 1.2 of the chapter.
Which of these is an example of an irrational number?
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√2
√2 was explicitly proven to be irrational in the chapter using a proof by contradiction.
What method was used to prove √2 is irrational?
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Proof by contradiction
The chapter specifically mentions using proof by contradiction to demonstrate the irrationality of √2.
What does the Fundamental Theorem of Arithmetic say about the order of prime factors?
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Order doesn't matter
The theorem states that prime factorization is unique, regardless of the order in which primes are written.
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