Homework Help

Can anyone help with the circled quesiton in the pic?  Thanks!

user profile pic

brandih | eNotes Employee

Posted September 12, 2013 at 5:38 PM via web

dislike 1 like

Can anyone help with the circled quesiton in the pic?  Thanks!

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

3 Answers | Add Yours

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted September 12, 2013 at 5:48 PM (Answer #1)

dislike 1 like

a) You need to convert the expression `sqrt3(2 + sqrt3)` into the form `a + bsqrt3` , hence, you need to open the brackets performing the required the multiplications, such that:

`sqrt3(2 + sqrt3) = 2*sqrt3 + sqrt3*sqrt3`

`sqrt3(2 + sqrt3) = 2*sqrt3 + 3`

Re-arranging the terms, yields:

`sqrt3(2 + sqrt3) = 3 + 2*sqrt3`

Comapring the resulted form `3 + 2*sqrt3` to the requested form `a + bsqrt3` and equating the like parts, yields:

`a = 3`

`b = 2`

Hence, converting the expression `sqrt3(2 + sqrt3)` into the form `a + bsqrt3` yields `3 + 2*sqrt3` .

b) You need to convert the expression `4 - sqrt3 - 2(1 - sqrt3)` into the form `a + bsqrt3` such that:

`4 - sqrt3 - 2(1 - sqrt3) = 4 - sqrt3 - 2 + 2sqrt3`

Grouping the terms that contains `sqrt 3` , yields:

`4 - sqrt3 - 2(1 - sqrt3) = (4 - 2) + (2sqrt3 - sqrt3)`

`4 - sqrt3 - 2(1 - sqrt3) = 2 + sqrt3`

Comapring the resulted form `2 + sqrt3` to the requested form `a + bsqrt3` and equating the like parts, yields:

`a = 2`

`b = 1`

Hence, converting the expression `4 - sqrt3 - 2(1 - sqrt3)` into the form `a + bsqrt3` yields `2 + sqrt3` .

user profile pic

abbypres123 | eNotes Newbie

Posted September 13, 2013 at 1:18 AM (Answer #2)

dislike 0 like

i don't know how to do this either but repost daily to find out it helps a  lot

user profile pic

tonys538 | TA , Undergraduate | (Level 1) Valedictorian

Posted September 30, 2014 at 4:57 PM (Answer #3)

dislike 0 like

The expressions `sqrt 3*(2+sqrt 3)` and `4 - sqrt 3 - 2*(1 - sqrt 3)` have to be expressed in the form `a + b*sqrt 3`

`sqrt 3*(2+sqrt 3)`

Open the brackets

`2*sqrt 3 + sqrt 3*sqrt 3`

= `2*sqrt 3 + 3`

= `3 + 2*sqrt 3`

`4 - sqrt 3 - 2*(1 - sqrt 3)`

Open the brackets

= `4 - sqrt 3 - 2 + 2*sqrt 3`

Simplify

= `2 + sqrt 3`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes