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(6 + root27)/(4 - root3) can be written in the form (r + sroot3)/13

(6 + root27)/(4 - root3) can be written in the form (r + sroot3)/13-example-1
User Gabriel Tomitsuka
by
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1 Answer

27 votes
27 votes

Answer:

r = 33 , s = 18

Explanation:

Rationalise the denominator by multiplying both numerator and denominator by the conjugate of the denominator.

The conjugate of 4 -
√(3) is 4 +
√(3) , then


((6+√(27))(4+√(3)) )/((4-√(3))(4+√(3)) ) ← expand numerator/denominator using FOIL

=
(24+6√(3)+4√(27)+√(81) )/(16+4√(3)-4√(3)-3 )

=
(24+6√(3)+4(3√(3)+9 )/(16-3)

=
(33+6√(3)+12√(3) )/(13)

=
(33+18√(3) )/(13)

with r = 33 and s = 18

User Scalpweb
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