Home
Class 9
MATHS
Prove that: 1/(3-sqrt(8))-1/(sqrt(8)-\ s...

Prove 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`

Text Solution

AI Generated Solution

To prove the expression \[ \frac{1}{3-\sqrt{8}} - \frac{1}{\sqrt{8}-\sqrt{7}} + \frac{1}{\sqrt{7}-\sqrt{6}} - \frac{1}{\sqrt{6}-\sqrt{5}} + \frac{1}{\sqrt{5}-2} = 5, \] we will rationalize each term in the expression step by step. ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • QUADRILATERALS

    RD SHARMA|Exercise All Questions|251 Videos

  • SURFACE AREA AND VOLUME OF A CUBOID AND CUBE

    RD SHARMA|Exercise All Questions|168 Videos

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

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`

  • (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))=?

    A
    0
    B
    1
    C
    `1/3`
    D
    5

    • Similar Questions

    Explore conceptually related problems

    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))) ?

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

    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

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

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

    Home
    Profile