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Prove that (2sqrt3+sqrt5) is an irration...

Prove that `(2sqrt3+sqrt5)` is an irrational number. Also check whether `(2sqrt3+sqrt5)(2sqrt3-sqrt5)` is rational or irrational.

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VGS PUBLICATION-BRILLIANT-REAL NUMBERS-EXERCISE
  1. Can the number 6^n, n being a natural number, end with the digit 5 ? G...

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  2. Is 7xx5xx3xx2+3 a composite number ? Justify your answer.

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  3. Prove that (2sqrt3+sqrt5) is an irrational number. Also check whether ...

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  4. If x^2 + y^2 = 6xy , prove that 2 log (x + y) = logx + logy + 3 log 2

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  5. Find the number of digit in 4^(2013), if log(10)2=0.3010.

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  6. Insert 4 rational numbers between 3/4 and 1 without using (a+b)/(2) fo...

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  7. If the prime factorization of a natural number (n) is 2^2xx3^2xx5^2xx7...

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  8. Find the value of log(5)125.

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  9. Write any two irrational numbers lying between 3 and 4.

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  10. Find the value of log(sqrt2) 256.

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  11. Find the HCF and LCM of 90, 144 by prime factorisation method.

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  12. Is log3 81 rational or irrational ? Justify your answer.

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  13. Expand log(10)385.

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  14. Find the HCF of 64 and 72

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  15. Find the value of logsqrt2 128.

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  16. Ramu says, "If log10 x = 0, value of x = 0". Do you agree with him ? G...

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  17. Write any three numbers of two digit its. Find the LCM and HCF for the...

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  18. Give an example for each of the following: (i) The product of two ir...

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  19. Give an example for each of the following: (i) The product of two ir...

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  20. State with reasons which of the following are rational numbers and whi...

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