Aussie Maths & Science Teachers: Save your time with SmarterEd
Expand and simplify `(sqrt5+2)(3 sqrt5-4)`. (2 marks)
`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`
Expand and simplify `(4sqrt(3)+sqrt(2))(4sqrt(8)-sqrt(12))`. (2 marks)
`30sqrt(6)-8`
`(4sqrt(3)+sqrt(2))(4sqrt(8)-sqrt(12))`
`=16sqrt(24)-4sqrt(36)+4sqrt(16)-sqrt(24)`
`=15sqrt(4xx6)-24+16`
`=30sqrt(6)-8`
Expand and simplify `(sqrt(20)+2sqrt(10))(3sqrt(6)-sqrt(3))`. (2 marks)
`4sqrt(30)+10sqrt(15)`
`(sqrt(20)+2sqrt(10))(3sqrt(6)-sqrt(3))`
`=3sqrt(120)-sqrt(60)+6sqrt(60)-2sqrt(30)`
`=3sqrt(4xx30)+5sqrt(4xx15)-2sqrt(30)`
`=6sqrt(30)+10sqrt(15)-2sqrt(30)`
`=4sqrt(30)+10sqrt(15)`
Find integers `a` and `b` by showing working to expand and simplify
`(3-sqrt2)^2 = a-b sqrt2`. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
`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`