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Show that: 1/(3-sqrt(8))-1/(sqrt(8)-sqrt...

Show that: `1/(3-sqrt(8))-1/(sqrt(8)-sqrt(7))+1/(sqrt(7)-sqrt(6))-1/(sqrt(6)-sqrt(5))+1/(sqrt(5)-2)=5`

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LHS
`1/(3-sqrt8)-1/(sqrt8-sqrt7)+1/(sqrt7-sqrt6)-1/(sqrt6-sqrt5)+1/(sqrt5-2)`
`(3+sqrt8)/(3^2-sqrt8^2)-(sqrt8+sqrt7)/(sqrt8^2-sqrt7^2)+(sqrt7+sqrt6)/(sqrt7^2-sqrt6^2)-(sqrt6+sqrt5)/(sqrt6^2-sqrt5^2)+(sqrt5+2)/(sqrt5-2^2)`
`3+sqrt3-sqrt8-sqrt7+sqrt7+sqrt8-sqrt6-sqrt5+sqrt5+2`
`5=RHS`.
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Show that: 1/((3-sqrt8))-1/((sqrt8-sqrt7))+1/((sqrt7-sqrt6))-1/((sqrt6-sqrt5))+1/((sqrt5-2))=5

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What is the value of (1/(sqrt(9) - sqrt(8)) - 1/(sqrt(8) - sqrt(7)) + 1/(sqrt(7) - sqrt(6)) - 1/(sqrt(6) - sqrt(5)) + 1/(sqrt(5) - sqrt(4))) ?

(1)/(sqrt(9)-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-sqrt(4))=?

(sqrt(6)+sqrt(5)+ 1/(sqrt(6)+sqrt(5)))^2

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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Solve: (1)/(sqrt(3)-8)-(1)/(sqrt(8)-sqrt(7))

RD SHARMA-RATIONALISATION -All Questions
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  2. If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt...

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  3. Show that: 1/(3-sqrt(8))-1/(sqrt(8)-sqrt(7))+1/(sqrt(7)-sqrt(6))-1/(sq...

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

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

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

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

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  8. Simplify the following expressions: (3+sqrt(3))(2+sqrt(2))

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  9. Simplify the following: (16)^(1/5)xx(2)^(1/5)

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

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  11. Simplify the following expressions: (4+sqrt(7))(3+sqrt(2))

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

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  13. Simplify : (sqrt(5)+sqrt(2))^2

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

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

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

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

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

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

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  20. Simplify each of the following: root(3)4xx root(3)(16) (ii) root(4)...

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