Home
Class 10
MATHS
Simplify: (3sqrt7)/(sqrt5 + sqrt2) - (5 ...

Simplify: `(3sqrt7)/(sqrt5 + sqrt2) - (5 sqrt5)/(sqrt2 + sqrt7) + (2 sqrt2)/(sqrt7 + sqrt5)`

Text Solution

Verified by Experts

Given expression `(3sqrt7)/(sqrt5 + sqrt2) - (5 sqrt5)/(sqrt2 + sqrt7) + (2 sqrt2)/(sqrt7 + sqrt5)`
`= (3 sqrt7)/(sqrt5 + sqrt2) xx (sqrt5 - sqrt2)/(sqrt5 - sqrt2) - (5sqrt5)/(sqrt2 + sqrt7) xx (sqrt2 - sqrt7)/(sqrt2 - sqrt7) + (2 sqrt2)/(sqrt7 + sqrt5) xx (sqrt7 - sqrt5)/(sqrt7 - sqrt5)`
`= (3 sqrt7 (sqrt5 - sqrt2))/((sqrt5)^(2) - (sqrt2)^(2)) - (5sqrt5 (sqrt2 - sqrt7))/((sqrt2)^(2) - (sqrt7)^(2)) + (2 sqrt2 (sqrt7 - sqrt5))/((sqrt7)^(2) - (sqrt5)^(2))`
`= (3 sqrt7 (sqrt5 - sqrt2))/(5-2) - (5 sqrt5 (sqrt2 - sqrt7))/(2-7) + (2 sqrt2 (sqrt7 - sqrt5))/(7 -5)`
`= (3 sqrt7 (sqrt5 -sqrt2))/(3) - (5sqrt5 (sqrt2 -sqrt7))/(-5) + (2 sqrt2 (sqrt7 - sqrt5))/(2)`
`= sqrt7 (sqrt5 - sqrt2) + sqrt5 (sqrt2 - sqrt7) + sqrt2 (sqrt7 - sqrt5)`
`= sqrt35 - sqrt14 + sqrt10 - sqrt35 + sqrt14 - sqrt10`
= 0
`:.` Given expression = 0
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC SURDS

    CALCUTTA BOOK HOUSE|Exercise Exercise -3.1|20 Videos

  • QUADRATIC SURDS

    CALCUTTA BOOK HOUSE|Exercise Exercise -3.2|28 Videos

  • QUADRATIC EQUATION IN ONE VARIABLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.5|40 Videos

  • RATIO AND PROPORTION

    CALCUTTA BOOK HOUSE|Exercise EXERCISE - 2.2 (Long Answer Type Questions)|19 Videos

Similar Questions

Explore conceptually related problems

(3sqrt7)/(sqrt5 + sqrt2) - (5sqrt5)/(sqrt2 + sqrt7) + (2sqrt2)/(sqrt7 + sqrt5) equals____

Simplify: (3 sqrt2)/(sqrt3 + sqrt6) - (4 sqrt3)/(sqrt6 + sqrt2) + (sqrt6)/(sqrt2 + sqrt3)

Answer any One question : Find the simplest value of : sqrt7(sqrt5 - sqrt2) - sqrt5(sqrt7 - sqrt2) + (2sqrt2)/(sqrt5+sqrt7)

Simplify : (3sqrt2)/(sqrt3 +sqrt6) -(4sqrt3)/(sqrt6 +sqrt2) +sqrt6/(sqrt2 +sqrt3)

Simplify: = (4 sqrt3)/(2 - sqrt2) - (30)/(4 sqrt3 - sqrt18) - (sqrt18)/(3-sqrt12)

Simplify : sqrt5/(sqrt2+sqrt3)-(3sqrt3)/(sqrt2+sqrt5)+(2sqrt2)/(sqrt3+sqrt5)

Simplify : (sqrt5+sqrt3)((3sqrt3)/(sqrt5+sqrt2)-sqrt5/(sqrt3+sqrt2))

Simplify: (1)/(sqrt2 +1) + (1)/(sqrt3 + sqrt2) + (1)/(sqrt4 + sqrt3)

Simplify : sqrt2 - sqrt(18) + sqrt(27) - sqrt(32)

CALCUTTA BOOK HOUSE-QUADRATIC SURDS-Exercise -3.2
  1. Simplify: (3sqrt7)/(sqrt5 + sqrt2) - (5 sqrt5)/(sqrt2 + sqrt7) + (2 sq...

    Text Solution

    |

  2. If x = root(3)(sqrt9 + 1) - root(3)(sqrt9-1), the value of x^(3) + 6x ...

    Text Solution

    |

  3. If x = 5 + 2 sqrt6 and xy =1, " then " (1)/(x^(2)) + (1)/(y^(2)) =

    Text Solution

    |

  4. The simpliest value of (sqrt5 (sqrt(3 - sqrt5)))/(sqrt2 + sqrt(7 - 3 s...

    Text Solution

    |

  5. (sqrt10 + sqrt18)/(sqrt18 - sqrt(3 - sqrt5)) =

    Text Solution

    |

  6. If sqrt2x = sqrt((sqrt3 + 1)/(sqrt3 -1)), then x^(2) -x=

    Text Solution

    |

  7. Rationalising factor of (root(3)(3) + root(3)(2)) is

    Text Solution

    |

  8. If (4 + sqrt15)^((3)/(2)) + (4 - sqrt15)^((3)/(2)) =k. sqrt10, then k ...

    Text Solution

    |

  9. If (sqrt(5 + 2sqrt6)- sqrt(5 - 2 sqrt6))/(sqrt(5 + 2 sqrt6)+ sqrt(5 - ...

    Text Solution

    |

  10. The value of sqrt(2+sqrt(2+ sqrt(2….oo))) is

    Text Solution

    |

  11. If x + 7 + 4 sqrt3, then sqrtx + (1)/(sqrtx) = 4

    Text Solution

    |

  12. root(5)((32)/(243)) is a surd

    Text Solution

    |

  13. show that (7)/(2^((1)/(2)) + 2^((1)/(4)) + 1) = 1 - 3.2^((1)/(4)) + 2....

    Text Solution

    |

  14. Write which one is a rational number and which one is a surd : root(6)...

    Text Solution

    |

  15. Express as like surds: root(6)(5), root(5)(6)

    Text Solution

    |

  16. Express as complete surds: 3 sqrt2, 2 root(3)(4)

    Text Solution

    |

  17. (a) If x gt a, y gt b and x + y = a + b, then find which one of (sqrtx...

    Text Solution

    |

  18. If x and y are rational and if x (3 + 2 sqrt2) - y sqrt2 = y(5 -3 sqrt...

    Text Solution

    |

  19. Rationalise the denominator: (a) (1)/(root(3)(3) + root(3)(2)), (b) ...

    Text Solution

    |

  20. Evaluate: (a) sqrt((x^(3))sqrt( y sqrt(x^(3)sqrt(y....oo)))) ,

    Text Solution

    |

  21. If 2x = a + sqrt((4b^(3) - a^(3))/(3a)) and 2y = a - sqrt((4b^(3) - a^...

    Text Solution

    |