smc-4228-70-Surds

Functions, 2ADV F1 2008 HSC 1e (Adapted)

Expand and simplify `(sqrt5+2)(3 sqrt5-4)`. (2 marks)

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

`7 + 2 sqrt 5`

Show Worked Solution

`(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)

Show Answers Only

`30sqrt(6)-8`

Show Worked Solution

`(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)

Show Answers Only

`4sqrt(30)+10sqrt(15)`

Show Worked Solution

`(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) ---

Show Answers Only

`a = 11,\ b = 6`

Show Worked Solution

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

Show Answers Only

`1 + 3 sqrt 3`

Show Worked Solution

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

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

`= 1 + 3 sqrt 3`