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Prove that (12)/(3 + sqrt5 - 2 sqrt2) = ...

Prove that `(12)/(3 + sqrt5 - 2 sqrt2) = 1 + sqrt5 + sqrt10 - sqrt2`

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`(3 + sqrt5 -2 sqrt2) (1 + sqrt5 + sqrt10 - sqrt2)`
`= 3 + sqrt5 - 2 sqrt2 + 3 sqrt5 + 5 -2 sqrt10 + 3 sqrt10 + 5sqrt2- 4sqrt5 - 3sqrt2 - sqrt10+4`
= 12
`:. 1 + sqrt5 + sqrt10 - sqrt2 = (12)/(3 + sqrt5 - 2 sqrt2)`
Hence, `(12)/(3 + sqrt5 -2 sqrt2) = 1 + sqrt5 + sqrt10 - sqrt2`
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CALCUTTA BOOK HOUSE-QUADRATIC SURDS-Exercise -3.1
  1. 5 root(5)(15625) =

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  2. sqrt27 + 3 sqrt75 - sqrt(243) + sqrt48 =

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  3. Between (sqrt6 + sqrt7) and (sqrt5 + sqrt8), the greater one is-

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  4. root(3)(8 (sqrt3 -1)^(3))=

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  5. sqrt(125) + 5 sqrt45 -2 sqrt(245) + sqrt20 = 8sqrt5

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  6. root(4)((81)/(256)) is a surd true or false

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  7. sqrt(192) and sqrt(147) are surds

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  8. sqrt(150) and sqrt(180) are surds

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  9. Express in the form of the product of a rational and irrational number...

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  10. Prove that (a) 3 sqrt48 - 4 sqrt75 + 5 sqrt(192) = 32 sqrt3 (b) sqrt...

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  11. Determine which of the followings are rational and which are surds: ...

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  12. Express in the form of like surds: root(3)(4), root(6)(5), 2sqrt3.

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  13. Express the followings in complete surds: 2 root(3)(4), aroot(p)(b)

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  14. Express the followings in the form of mixed surds: root(5)(-2187 a^(6)...

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  15. Find out the greatest and least numbers: 2sqrt2, 3root(3)(2), 2root(4)...

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  16. Which one is greater between (sqrt7 - sqrt5) and (sqrt13 - sqrt11) ?

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  17. Which one is greater between (sqrt11 + sqrt9) and (sqrt13 + sqrt7) ?

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  18. Evaluate : (a) sqrt(xsqrt(xsqrt(x.....oo))) (b) sqrt(6+ sqrt(6 + sqrt(...

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  19. Prove that (a) sqrt(-sqrt3 + sqrt(3 + 8 sqrt(7 + 4 sqrt3))) =2 (b) ...

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  20. Prove that (12)/(3 + sqrt5 - 2 sqrt2) = 1 + sqrt5 + sqrt10 - sqrt2

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