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Show that (sqrt5 + sqrt3)/(sqrt5 - sqrt3...

Show that `(sqrt5 + sqrt3)/(sqrt5 - sqrt3) - (sqrt5 - sqrt3)/(sqrt5 + sqrt3) = 2 sqrt15`

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LHS `= (sqrt5 + sqrt3)/(sqrt5 - sqrt3) - (sqrt5 -sqrt3)/(sqrt5 + sqrt3) = ((sqrt5 + sqrt3)^(2) - (sqrt5 - sqrt3)^(2))/((sqrt5 - sqrt3) (sqrt5 + sqrt3))`
`= (4.sqrt5.sqrt3)/((sqrt5)^(2) - (sqrt3)^(2)) = (4 sqrt15)/(5 -3) = (4sqrt15)/(2) = 2sqrt15`= RHS.
`:. (sqrt5 + sqrt3)/(sqrt5 - sqrt3) - (sqrt5 - sqrt3)/(sqrt5 + sqrt3) = 2 sqrt15`
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CALCUTTA BOOK HOUSE-QUADRATIC SURDS-Exercise -3.2
  1. Show that (sqrt5 + sqrt3)/(sqrt5 - sqrt3) - (sqrt5 - sqrt3)/(sqrt5 + s...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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