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Express (√5+4)/(√5-2) in the form p+q√5 where p and q are integers.

Rationalise the denominator by multiplying the whole fraction by (√5+2)/(√5+2). This is equal to one and this removes the surd from the denominator of the fraction, allowing us to solve it.

This gives us
(5+4√5+√5+4)/(5-4) 
which is equal to
(9+5√5)/1

Which gives us 9+5√5.

So p=9 and q=5

Fern H. A Level Maths tutor, GCSE Maths tutor

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