Real Number

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Across
  1. 4. Square root of P is irrational, where p is _____.
  2. 6. Every composite number can be expressed (factorized) as a product of primes, and this factorization is unique, apart fro the order in which the prime factor occurs. This is which theorem of Arithmetic?
  3. 8. Pi is ____.
  4. 10. Euclid's division is a technique to compute ______ of two positive numbers.
Down
  1. 1. Given two posetive integers a and b, there exist unique integers q and r satifying a = bq + r, 0 = r<b. This is which lemma.
  2. 2. Let x=p/q be a rational number, such that the factorization of q is of the form 2^n5^m, where m and n are non negative integers. Then x has a decimal expansion which is _____.
  3. 3. For any two posetive integers a and b, HCF (a,b) x LCM (a,b) = _____ of the numbers.
  4. 5. A proven statement used for proving another statement.
  5. 7. Prime factorisation of a natural number is _____.
  6. 9. A series of well defined steps.