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Show that:1/((3-sqrt8))-1/((sqrt8-sqrt7)...

Show that:`1/((3-sqrt8))-1/((sqrt8-sqrt7))+1/((sqrt7-sqrt6))-1/((sqrt6-sqrt5))+1/((sqrt5-2))=5`

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

Find the value of the expression: 1/(3-sqrt(8)) - 1/(sqrt(8)-sqrt(7)) + 1/(sqrt(7)-sqrt(6)) - 1/(sqrt(6)-sqrt(5)) +1/(sqrt(5) - sqrt(4))

Knowledge Check

  • Let T = (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7)) +(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)+2) then-

    A
    `T lt 1`
    B
    `T = 1`
    C
    `1 lt T lt 2`
    D
    `T lt 2`

  • The value of [1/(sqrt9-sqrt8)]-[1/(sqrt8-sqrt7)]+[1/(sqrt7-sqrt6)]-[1/(sqrt6-sqrt5)]+[1/(sqrt5-sqrt4)] is A)6 B)5 C)-7 D)-6

    A
    6
    B
    5
    C
    `-7`
    D
    `-6`

    • Similar Questions

    Explore conceptually related problems

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

    (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5

    (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5

    (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=

    (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7))-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5

    (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)) is equal to

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