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Prove that: 1/(1+sqrt(2))+1/(sqrt(2)+sqr...

Prove that: `1/(1+sqrt(2))+1/(sqrt(2)+sqrt(3))+1/(sqrt(3)+\ sqrt(4))+1/(sqrt(4)+sqrt(5))+1/(sqrt(5)+sqrt(6))+1/(sqrt(6)+sqrt(7))+\ 1/(sqrt(7)+sqrt(8))+1/(sqrt(8)+sqrt(9))=2`

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RD SHARMA ENGLISH-RATIONALISATION -All Questions
  1. Simplify: (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+\ 2)/(sqrt(5)-\ 2)

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  2. Prove that: 1/(3-sqrt(8))-1/(sqrt(8)-\ sqrt(7))+1/(sqrt(7)-\ sqrt(6))-...

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  3. Prove that: 1/(1+sqrt(2))+1/(sqrt(2)+sqrt(3))+1/(sqrt(3)+\ sqrt(4))+1/...

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  4. If x=2+sqrt(3) , find the value of x^2+1/(x^2)

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  5. If x=3-2sqrt(2),find x^2+1/(x^2)

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  6. If x=1-sqrt(2) , find the value of (x-1/x)^3

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  7. If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt...

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  8. If a=(2-sqrt(5))/(2+sqrt(5)) and b=(2+sqrt(5))/(2-sqrt(5)), find a^2-b...

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  9. If x=1/(2-sqrt(3)), find the value of x^3-2x^2-7x+5

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  10. Evaluate : (15)/(sqrt(10)+sqrt(20)+sqrt(40)-sqrt(5)-sqrt(80)), is bei...

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  11. Rationalise the denominator of each of the following (i)3/(sqrt(5))...

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  12. Rationalise the denominator of each of the following (i)1/(sqrt(12)...

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  13. Rationalise the denominator of each of the following (i)(sqrt(3)+\ ...

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  14. Find the value to three places of decimals of each of the following....

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  15. Find the value to three places of decimals of each of the following....

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  16. Find the value to three places of decimals of each of the following....

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  17. Express each one of the following with rational denominator: (i)1...

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  18. Express each one of the following with rational denominator: (i)(30...

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  19. Express each one of the following with rational denominator: (i)(sqr...

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  20. Express each one of the following with rational denominator: (i)(3s...

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