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Use Euclid's division lemma to show that...

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. [Hint : Let x be any positive integer then it is of the form 3q, 3q+1 or 3q+2. Now square each of these and show that they can be rewritten in the form 3m or 3m+1].

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SUBHASH PUBLICATION-REAL NUMBER-EXERCISE 8.4
  1. Use Euclid's division lemma to show that the square of any positive in...

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  2. Without actually performing the long division state whether the follow...

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  3. Without actually performing the long division state whether the follow...

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  4. Without actually performing the long division state whether the follow...

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  5. Without actually performing the long division state whether the follow...

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  6. Without actually performing the long division state whether the follow...

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  7. Without actually performing the long division state whether the follow...

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  8. Without actually performing the long division state whether the follow...

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  9. Without actually performing the long division state whether the follow...

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  10. Without actually performing the long division state whether the follow...

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  11. Without actually performing the long division state whether the follow...

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  12. Write down the decimal expansions of 13/3125

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  13. Write down the decimal expansions of 17/8

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  14. Write down the decimal expansions of 15/1600

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  15. Write down the decimal expansions of 6/15

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  16. Write down the decimal expansions of 23/(2^(3) times 5^(2))

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  17. Write down the decimal expansions of 35/50

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  18. The following real numbers have decimal expansions as given below. In ...

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  19. The following real numbers have decimal expansions as given below. In ...

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  20. The following real numbers have decimal expansions as given below. In ...

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