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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 each of the following : (i) 3/(5-sqrt(3))+2/(5+sqrt(3)) (i...

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

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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. Simplify : (i)(5+sqrt(5))(5-sqrt(5)) (ii) (3+2sqrt(2))(3-2sqrt(2)...

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  5. Simplify the following expressions: (i)(3+sqrt(3))(2+sqrt(2)) (ii...

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  6. Simplify each of the following: (i)(16)^(1/5)xx(2)^(1/5) (ii) (243)...

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  7. Simplify the following expressions: (i)(11+sqrt(11))(11-sqrt(11)) ...

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  8. Simplify the following expressions: (i) (4+sqrt(7))(3+sqrt(2)) (ii)...

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  9. Simplify each of the following: (i) 4 3×16 3 (ii) (1250 4)/(2 4)

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  10. Simplify : (i)(sqrt(5)+sqrt(2))^2 (ii) (sqrt(11)-sqrt(5))^2

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  11. Rationalise the denominator of 2/(sqrt(3)) .

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  12. Simplify the following expressions: (i)(sqrt(3)+sqrt(7))^2 (ii) ...

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  13. Simplify each of the following: (i)root(5)(16)xxroot(5)(2) (ii) ro...

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  14. Simplify the following expressions: (i)(3+sqrt(3))\ (2+sqrt(2)) (...

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  15. Simplify: (i)(5+\ sqrt(5))\ (5-\ sqrt(5)) (ii) (3+2sqrt(2))\ (3-2...

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  16. Simplify : (i)(sqrt(5)+sqrt(2))^2 (ii) (sqrt(11)-sqrt(5))^2

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  17. Simplify each of the following: (i)root(3)4xx root(3)(16) (ii) ro...

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  18. Simplify the following expressions: (i)\ (4+\ sqrt(7))\ (3+sqrt(2)) ...

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  19. Simplify the following expressions: (i)\ (11+sqrt(11))\ (11-\ sqrt(11...

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  20. Simplify the following expressions: (i)(3+sqrt(3))\ (3-sqrt(3)) (...

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