1. ( 8 + square root 5) (8- square root 5)
2. Create your own binomial expression with a radical in the second term.

Part 1: Identify its conjugate and explain, in complete sentences, why it is the conjugate.

Part 2: Multiply your original binomial expression and its conjugate. What happened to the radicals and why?

Question

1. ( 8 + square root 5) (8- square root 5)
2. Create your own binomial expression with a radical in the second term. 

Part 1: Identify its conjugate and explain, in complete sentences, why it is the conjugate. 

Part 2: Multiply your original binomial expression and its conjugate. What happened to the radicals and why?

anonymous · Answer

did you do #1?

anonymous · Answer

no :/

anonymous · Answer

do you know how to FOIL it out?

anonymous · Answer

I'm having trouble with that :/

anonymous · Answer

1. Use the property -> (a+b)(a-b) = a^2 - b^2 .. 

2. Radical in the second term is -- sqrt 5 .. So and expression using it could be .. 
$$3 + \sqrt 5$$ ... (you may make anyone of your choice..)

(i) conjugate of 3+ sqrt 5 = 3 - sqrt 5

(ii) When you multiply these two, you get .. $$(2+\sqrt 5)(2-\sqrt 5)$$
$$=> 3^2 - (\sqrt5)^2 = 9-5  = 4$$

anonymous · Answer

oh, I should let you know that each problem is NOT related to each other in any way, they're different

anonymous · Answer

would the answer to the first question be 64 - 18 square root 5 ???

anonymous · Answer

they sort of are related because your second question talks about the conjugate of a binomial...  the conjugate of (a+b) is (a-b).... and vice/versa...

anonymous · Answer

well yes, but I mean they aren't suppose to go together if you know what I mean. And for the first question, is my answer correct??

anonymous · Answer

no...

anonymous · Answer

use the formula @Aditi_Singh  , stated:  $\large (a+b)(a-b) = a^2 - b^2 $

anonymous · Answer

multiplying conjugates will always give you difference of squares....

anonymous · Answer

$\large (8+\sqrt5)(8-\sqrt5)=8^2-(\sqrt5)^2 $

anonymous · Answer

ohh. when I re-did it, I got 59- 16 square root of 5, idk if thats right...

anonymous · Answer

$\large (8+\sqrt5)(8-\sqrt5)=8^2-(\sqrt5)^2=64-5 $

anonymous · Answer

=59

anonymous · Answer

oh it is 59, I did it that way the first time and wasn't sure if it was right bc I didn't get a square root

anonymous · Answer

now to do the second part do the same thing...
change the 8 to any number you want.. and change that $\sqrt5 $ to any radical you want...
then do the same thing we just did on the one you created....:)

anonymous · Answer

Believe me or not.. but i really think that the 1st and the 2nd ques are related to each other.. in some way!

anonymous · Answer

thanks guys, I just figured out how to do the second one lol. and they kinda are related loll