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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 of the form `5n or 5n+1 or 5n+4,` where n is a whole number.

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Use Euclid's division lemma to show that the square of any positive integer is of the form 3p, 3p+1.

Use Euclid's division lemma to show that the cube of any positive integer is of the form 7m or 7m+1 or 7m+6 .

Use Euclid's division lemma, to show that the cube of any positive integer is of the form 3p or 3p+1 or 3p+2 for any integer 'p'.

Use Euclid division lemma to show that any positive even integer is of the form 6q or 6q+2 or 6q+4, where q is some intergers.

Use Euclid division lemma to show that any positive odd integer is of the form 6q+1 or 6q+5 , where q is some integers.

Use Euclid division Lemma to show that any positive even integer is of the form. 2q or 2q+2 or 2q+4 where q is some integer.

Use Euclid division Lemma to show that any positive even interger is of the form 4q or 4q+2 or 4q+4 when q is some integer.

Show that cube of any positive integer will be in the form of 8m or 8m + 1 or 8m + 3 or 8m + 5 or 8m + 7 , where m is a whole number.

Use Euclids division lemma to show that the cube of positive integer is of the form 9m,9m+1 or 9m+8. (OR) Show that the cube of any positive integer is of form 9m or 9m+1 or 9m+8 , where m is an integer.

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VGS PUBLICATION-BRILLIANT-REAL NUMBERS-EXERCISE
  1. Use Euclid's division lemma, to show that the cube of any positive int...

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  2. Prove that sqrt3-sqrt5 is an irrational number.

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  3. Use Euclid's division lemma to show that the square of any positive in...

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  4. Use Euclid's division lemma to show that the square of any positive in...

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  5. If x^2+y^2=27xy, then show that log((x-y)/(5))=1/2[logx+logy].

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  6. Prove that sqrt3 + sqrt5 is an irrational number.

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  7. Show that cube of any positive integer will be in the form of 8m or 8m...

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  8. Prove that sqrt2+sqrt11 is an irrational number.

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  9. Show that sqrt5-sqrt3 is an irrational number.

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  10. Write 210 as product of prime factors.

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  11. If the HCF of 306 and 657 is 9 then find their LCM.

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  12. Support the Fundamental theorem of Arithmetic by considering some exam...

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  13. Is the units digit in the value of 6^n where 'n' is a natural number i...

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  14. Explain why 7xx11xx13+13 and 7xx6xx5xx4xx3xx2xx1+5 are composite nubme...

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  15. Find the HCF of 45,75 from Euclid's division lemma.

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  16. How do you say 7xx11xx13+13 and 7xx6xx5xx4xx3xx2xx1+5 are composite nu...

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  17. Express the following in log forms. (i) 2^(5)=32

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  18. Express the following in log forms. (ii) 3^(3)=27

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  19. Express the following in log forms. (iii) 5^(3)=125

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  20. Calculate the value of log(2)512.

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