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Show that the square of any positive int...

Show that the square of any positive integer is of the form 4m or 4m + 1 for some integer m.

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KUMAR PRAKASHAN-REAL NUMBERS -TEST YOUR SKILLS
  1. Show that the square of any positive integer is of the form 4m or 4m +...

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  2. Show that the square of any positive integer cannot be of the form 6m ...

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  3. Show that the cube of any positive integer j is of the form 4m or 4m +...

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  4. if n is an odd integer, then show that n^(2) - 1 is divisible by 8.

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  5. Using Euclid’s division algorithm, find the HCF of 441, 567 and 693.

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  6. Using Euclid’s division algorithm, find the largest number that divide...

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  7. Using Euclid’s division algorithm, find the HCF of 5404 and 4800

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  8. Using Euclid’s division algorithm, find the HCF of 1620, 1725 and 255.

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  9. For any positive integer n, prove that n^(3) - n is divisible by 6.

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  10. Find the missing numbers a, b, c and d in the following factor tree

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  11. Find the HCF of 525 and 1120 by the prime factorisation method. Then, ...

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  12. The HCF of 128 and 68 is expressible in ? the form 128 m - 1 5 x 6 8 ....

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  13. Explain why 5 x 7 x 13 + 13 is a composite number

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  14. The HCF of two numbers is 145 and their LCM is 2175. If one of the nu...

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  15. Find the HCF and LCM of 510 and 92 and also verify that HCF x LCM = th...

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  16. Find the HCF and LCM of 60, 120 and 288.

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  17. Prove that 3 +2 sqrt(5) is irrational.

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  18. Prove that sqrt(3) + sqrt(5) is irrational.

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  19. Prove that sqrt(11) is irrational.

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  20. Prove that 5sqrt(7) is irrational.

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