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Expand and simplify `(sqrt5+2)(3 sqrt5-4)`. (2 marks)
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`7 + 2 sqrt 5`
`(sqrt 5+2)(3 sqrt 5-4)`
`= 3 sqrt 5 xx sqrt 5-4 sqrt 5 + 6 sqrt 5-8`
`= 3 xx 5-4 sqrt 5 + 6 sqrt 5-8`
`= 15-4 sqrt 5 + 6 sqrt 5-8`
`= 15-8 + 2 sqrt 5`
`= 7 + 2 sqrt 5`
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`
| `(3-sqrt2)^2` | `= 9-6 sqrt2 + (sqrt2)^2` |
| `= 9-6 sqrt2 + 2` | |
| `= 11-6 sqrt2` | |
| `:.\ a = 11, \ \ b = 6` | |
Expand and simplify `(sqrt3-1)(2 sqrt3 + 5)`. (2 marks)
`1 + 3 sqrt 3`
`(sqrt 3-1)(2 sqrt 3 + 5)`
`= 2 xx 3 + 5 sqrt 3-2 sqrt 3-5`
`= 1 + 3 sqrt 3`