Question

2√3(3+√5)(1-√5)/(1+√5)

Answer 1

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2√3 ( 3 + √5 ) ( 1 - √5 ) / ( 1 + √5 )
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by rationalizing denominator of given irrational number , we get

= 2√3( 3+√5 ) ( 1 - √5 ) /(1 +√5)×( 1 - √5 )/(1 -√5)

= 2√3 ( 3 + √5 ) ( 1 - √5 )^2 / ( 1 - 5 )

= -2√3/ 4 [ ( 3 + √5 ) ( 1 + √5 - 2√5 ) ]

= -√3 /2 [3 + 3√5 - 6√5 + 5 - 10 ]

= -√3 / 2 [ - 3√5 - 2 )

= 1 / 2( 3 √15 + 2√3 )

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Your Answer : 1/ 2 ( 3√15 + 2√3 )
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