SOLUTION: Rationalize the denominator (√ 7)/(√ 3+2) I got as far as (√ 7)/(√ 3+2) * (√ 3-2)/(√ 3-2) [(√ 7)(√ 3+2)]/(√ 3)^2-(2)^2

Algebra ->  Radicals -> SOLUTION: Rationalize the denominator (√ 7)/(√ 3+2) I got as far as (√ 7)/(√ 3+2) * (√ 3-2)/(√ 3-2) [(√ 7)(√ 3+2)]/(√ 3)^2-(2)^2       Log On


   

Question 1058454: Rationalize the denominator
(√ 7)/(√ 3+2)
I got as far as
(√ 7)/(√ 3+2) * (√ 3-2)/(√ 3-2)
[(√ 7)(√ 3+2)]/(√ 3)^2-(2)^2
[(√ 7)(√ 3+2)]/3+4
[(√ 7*√3)-(2√2)]/7
[(√21)-(2√2)]/7
My book is saying that the answer is (√21)-(2√2) Without a denominator. Did I do something wrong or is the book wrong (it's been wrong before).
Found 3 solutions by Fombitz, Alan3354, Edwin McCravy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Your denominator should be 3-4 not 3%2B4
%28sqrt%283%29%2B2%29%28sqrt%283%29-2%29=3-2sqrt%283%29%2B2sqrt%283%29-4=3-4=-1
Final answer should be,
sqrt%287%29%282-sqrt%283%29%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%287%29%2F%28sqrt%283%29%2B2%29
= sqrt%287%29%2A%28sqrt%283%29-2%29%2F%28%28sqrt%283%29-2%29%2A%28sqrt%283%29%2B2%29%29
= %28sqrt%2821%29+-+2sqrt%287%29%29%2F%283+-+4%29 You had 3+4
= %28sqrt%2821%29+-+2sqrt%287%29%29%2F-1
= 2sqrt%287%29+-+sqrt%2821%29
============
The book is also wrong.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Looks like you made a sign error, 3+4 should have been 3-4.
Multiply the bottoms using FOIL

sqrt%287%29%2F%28sqrt%283%29%2B2%29

%28sqrt%287%29%2F%28sqrt%283%29%2B2%29%29%2A%28%28sqrt%283%29-2%29%2F%28sqrt%283%29-2%29%29

%28sqrt%287%29%2A%28sqrt%283%29-2%29%29%2F%28%28sqrt%283%29%2B2%29%28sqrt%283%29-2%29%29

Use FOIL in the denominator:



[That was where you made your error]

%28sqrt%2821%29-2sqrt%287%29%29%2F%283-2sqrt%283%29%2B2sqrt%283%29-4%29%29



%28sqrt%2821%29-2sqrt%287%29%29%2F%283-4%29%29

%28sqrt%2821%29-2sqrt%287%29%29%2F%28-1%29

%28sqrt%2821%29-2sqrt%287%29%29%2F%28-1%29%22%22%2A%22%22%28-1%29%2F%28-1%29

%28-sqrt%2821%29%2B2sqrt%287%29%29%2F1

2sqrt%287%29-sqrt%2821%29

Yes the book is wrong!

Edwin