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Euclid Division lemma

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Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

RS AGGARWAL-REAL NUMBERS-Exercise 1E
  1. Euclid Division lemma

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  2. State Fundamental Theorem of Arithmetic.

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  3. Express 360 as product of its prime factors.

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  4. If a and b are two prime numbers then find HCF ( a,b)

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  5. If a and b are two prime numbers then find LCM (a,b)/

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  6. If the product of two numbers is 1050 and their HCF is 25, find their ...

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  7. What is a composite number ?

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  8. If a and b are relavtively prime then what is their HCF ?

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  9. If the rational number a/b has a terminating decimal expansion, what ...

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  10. Simplify : ((2 sqrt(45) + 3 sqrt(20)))/(2sqrt5)

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  11. Write the decimal expainsion of 73/ (((2^(4) xx 5^(3)))

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  12. show that there is no value of n for which ( 2^(n) xx 5 ^(n)) ends i...

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  13. Is it possible to have two numbers whose HCF is 25 and LCM is 520 ?

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  14. Give an example of two irrationals whose sum is rational.

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  15. Give an example of two irrationals whose product is rational.

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  16. If a and b are relavtively prime, what is their LCM ?

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  17. The LCM of two numbers is 1200. show that the HCF of these numbers can...

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  18. Express 0.overline(4) as a rational number in simplest form.

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  19. Express 0.overline(23) as a rational number is simplest form.

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  20. Explain why 0./155001500015 …. Is an irrational number.

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