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Rationalize the denominator of (sqrt(5)+sqrt(2))/(sqrt(5)-sqrt(2)). The answer can be written as (A+Bsqrt(C))/D, where A, B, C, and D are integers. D is positive and C is not divisible by the square of any prime. If the greatest common divisor of A, B, and D is 1, find A+B+C+D.

 Jun 15, 2019
 #1
avatar+106993 
+6

\(\frac{\sqrt5+\sqrt2}{\sqrt5-\sqrt2}\)

 

the bottom is sqrt5 - sqrt 2

You just have to multiply both the top and the bottom by sqrt5 sqrt2    

 

That fact that the top is the same is just a coincidence. 

 Jun 15, 2019
 #2
avatar+21 
+2

I’m confused. Don’t you have to find A+B+C+D?

 Jun 15, 2019
 #7
avatar+106993 
+2

Did you do the multiplication as I told you too or did not want to do any of the working or thinking for yourself?

Melody  Jun 16, 2019
 #3
avatar+106535 
+5

√5 + √2      [ √5 + √2 ]            5 + 2√10 + 2                  7 + 2√10

______      _________ =      _____________ =         _________

√5 - √2       [ √5 +  √2 ]                5    -   2                            3

 

A + B  + C  +  D  =

 

7 + 2 + 10 + 3  =

 

22

 

CORRECTED

 

 

cool cool cool

 Jun 15, 2019
edited by CPhill  Jun 15, 2019
 #4
avatar
+2

CPhill: Your final answer should read:
[7 + 2sqrt(10)] / 3

 Jun 15, 2019
 #5
avatar+106535 
+2

THX, Guest.....careless error  !!

 

cool cool cool

CPhill  Jun 15, 2019
 #6
avatar+106993 
+2

Why did you vote my answer down Hectictar?

Do you think people should be spoon fed all their answers?

Is a good hint worse than no answer at all?

I am not cross, I am just disillusioned with the site in general.

 Jun 16, 2019
 #8
avatar+8848 
+3

I'm sorry Melody. I did give your answer a point but then took it back off a few seconds later. To be honest, I can't give you a good reason why I did that. I don't really remember what I was thinking, but maybe it was to make yours and CPhill's answer have equal number of points. I don't think that I had a good reason.

hectictar  Jun 16, 2019
 #9
avatar+106993 
+2

Ok that is a good enough reason.

I should not have mentioned it anyway. :) 

Melody  Jun 16, 2019

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