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Prove that ( 4-5 sqrt2) is an irrationa...

Prove that ` ( 4-5 sqrt2)` is an irrational number.

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RD SHARMA-REAL NUMBERS-All Questions
  1. Show that 2-sqrt(3) is an irrational number.

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  2. Show that 3+sqrt(2) is an irrational number.

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  3. Prove that ( 4-5 sqrt2) is an irrational number.

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  4. Show that 5-2sqrt(3) is an irrational number.

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  5. Prove that 2sqrt(3)-1 is an irrational number

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  6. Prove that 2-3sqrt(5) is an irrational number.

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  7. 4. Prove that sqrt(3)+sqrt(5) is irrational.

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  8. Prove that sqrt(3)+sqrt(4) is an irrational number.

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  9. If p ,\ q are prime positive integers, prove that sqrt(p)+sqrt(q) i...

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  10. Without actually performing the long division, state whether the fo...

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  11. Without actually performing the long division, state whether the fo...

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  12. Without actually performing the long division, state whether the fo...

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  13. Without actually performing the long division, state whether the fo...

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  14. Write down the decimal expansions of the following rational numbers...

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  15. Write down the decimal expansions of the following rational numbers...

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  16. What can you say about the prime factorisations of the denominators...

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  17. State Fundamental Theorem of Arithmetic.

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  18. Write 98 as product of its prime factors.

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  19. Write the exponent of 2 in the prime factorization of 144.

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  20. Write the sum of the exponents of prime factors in the prime factor...

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