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Simplify each of the following by ration...

Simplify each of the following by rationalising the denominator; `1/(5+sqrt(2))` (ii) `(5+sqrt(6))/(5-sqrt(6))` `(7+3sqrt(5))/(7-3sqrt(5))` (iv) `(2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))`

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The correct Answer is:
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(i) `(5+sqrt(6))/(5-sqrt(6))=(5+sqrt(6))/(5-sqrt(6))xx(5+sqrt(6))/(5+sqrt(6))`
`=((5)^(2)+(sqrt(6))^(2)+2(5)(sqrt(6)))/((5)^(2)-(sqrt(6)))=(25+6+10sqrt(6))/(25-6)=(31+10sqrt(6))/(19)`
(ii) `(7-3sqrt(5))/(7+3sqrt(5))=(7-3sqrt(5))/(7+3sqrt(5))xx(7-3sqrt(5))/(7-3sqrt(5))=((7)^(2)+(3sqrt(5))^(2)-2(7)(3sqrt(5)))/((7)^(2)-(3sqrt(5))^(2))`
`=(49+45-42sqrt(5))/(49-45)=(94-42sqrt(5))/(4)=(47-21sqrt(5))/(2)`
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