smc-983-20-Surds (General)

Functions, 2ADV F1 2004 HSC 1d

Find integers `a` and `b` by showing working to expand and simplify

`(3-sqrt2)^2 = a-b sqrt2`. (2 marks)

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`a = 11,\ b = 6`

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Expand and simplify `(sqrt3-1)(2 sqrt3 + 5)`. (2 marks)

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`1 + 3 sqrt 3`

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`(sqrt 3-1)(2 sqrt 3 + 5)`

`= 2 xx 3 + 5 sqrt 3-2 sqrt 3-5`

`= 1 + 3 sqrt 3`