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Show that the square of any positive int...

Show that the square of any positive integer cannot be of the form (5q+2) or (5q+3) for any integer q.

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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.

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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  3. Prove that sqrt5 is an irrational number.

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  4. Prove that 2+5sqrt3 is an irrational number, given that sqrt3 is an ir...

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  5. Prove that sqrt2 is an irrational number.

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  13. Show that the square of any positive odd integer is of the form 8m+1, ...

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  14. Prove that sqrtp+sqrtq is irrational, where p and q are primes.

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  15. Prove that 3+2sqrt5 is irrational number.

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  16. Show that the square of any positive integer cannot be of the form (5q...

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  17. Prove that one of every three consecutie positive integers is divisble...

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  18. Prove that sqrtn is not a rational number, if n is not perfect square.

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