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Simplify: = (4 sqrt3)/(2 - sqrt2) - (30)...

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

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Given expression `= (4 sqrt3)/(2 - sqrt2) - (30)/(4 sqrt3 - sqrt18) - (sqrt18)/(3-sqrt12)`
`= (4 sqrt3 (2 sqrt2))/((2 - sqrt2) (2 + sqrt2)) - (30 (4 sqrt3 + sqrt18))/((4sqrt3 - sqrt18) (4 sqrt3 + sqrt18)) - (sqrt18 (3 + sqrt12))/((3-sqrt12) (3 + sqrt12))`
`= (4 sqrt3 (2 + sqrt2))/((2)^(2) - (sqrt2)^(2)) - (30 (4 sqrt3 + sqrt18))/((4sqrt3)^(2) - (sqrt18)^(2)) - (sqrt18 (3 + sqrt12))/((3)^(2) - (sqrt12)^(2))`
`= (4 sqrt3 (2 + sqrt2))/(4-2) - (30(4 sqrt3 + sqrt18))/(48 - 18) - (sqrt18 (3 + sqrt12))/(9 - 12)`
`= (4 sqrt3 (2 + sqrt2))/(2)- (30 (4 sqrt3 + sqrt18))/(30) - (sqrt18 (3 + sqrt12))/(-3)`
`= 2 sqrt3 (2 + sqrt2) - (4 sqrt3 + 3 sqrt2) - (3 sqrt2 (3 + 2 sqrt3))/(-3)`
`=4 sqrt3 + 2 sqrt6 - 4sqrt3 - 3sqrt2 + 3sqrt2 + 2 sqrt6`
`=4 sqrt6`
Hence the given expression `= 4 sqrt6`
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CALCUTTA BOOK HOUSE-QUADRATIC SURDS-Exercise -3.2
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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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