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blackjesus619
 2 years ago
Express 7+√5/3+√5 in the form a+b√5 where a and b are intergers
blackjesus619
 2 years ago
Express 7+√5/3+√5 in the form a+b√5 where a and b are intergers

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hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1do you know how to rationalize the denominator ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1multiply the numerator and denominator by the conjugate of denominator here, it'll be 3 \(\sqrt5\) what do u get ?

blackjesus619
 2 years ago
Best ResponseYou've already chosen the best response.0What do u get when u multiply it with 7+√5

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1you mean multiply (1+√5) with (3√5) thats your numerator, you just need to foil to simply it.

blackjesus619
 2 years ago
Best ResponseYou've already chosen the best response.0Its 7√5 in the question can't multiply it with 3√5 that's the part I get confused with

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1ok, \(7\sqrt 5 \times 3 = 21 \sqrt 5\ \\7\sqrt5\times \sqrt5= 7\sqrt{5^2}=7\times 5=35 \\so \\ 7\sqrt5(3\sqrt5)=21\sqrt535 \) got it ?

blackjesus619
 2 years ago
Best ResponseYou've already chosen the best response.0The answer on my answer sheet is 4√5 how do I get that

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1ok, then we were supposed to multiply (7+√5) (and not 7√5 as you mentioned "Its 7√5 in the question") then you actually foil : \((7+√5)(3√5)= 7*3 7√5+3√5√5√5 = 21+(7+3)√55\\=164√5=4(4√5)\) and if you simplify the denominator, you'll get a 4 which cancels with the numerator's 4 and you are just left with 4√5

blackjesus619
 2 years ago
Best ResponseYou've already chosen the best response.0I didn't get anything from that sorry but u have confused me a lot

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1i used this \((a+b)(c+d)=ac+ad+bc+bd\) try to do this with (7+√5)(3√5) take 7 multiply it with 3 and √5 then take √5, multiply it with 3 and √5

phi
 2 years ago
Best ResponseYou've already chosen the best response.1to go over it: \[ \frac{ 7+\sqrt{5}}{3+\sqrt{5}} \] you multiply top and bottom by \( 3 \sqrt{5} \) \[ \frac{ (7+\sqrt{5})( 3 \sqrt{5})}{(3+\sqrt{5})( 3 \sqrt{5})} \]

phi
 2 years ago
Best ResponseYou've already chosen the best response.1now you have two FOIL problems: one on the top and one in the bottom can you do them ? (see hartn's posts on how)

blackjesus619
 2 years ago
Best ResponseYou've already chosen the best response.0I don't know how to do the 7+√5 one

phi
 2 years ago
Best ResponseYou've already chosen the best response.1to do \[ (7+ \sqrt{5})(3 \sqrt{5} ) \] you do 4 multiplies: the First, Outer, Inner, Last This might help http://www.khanacademy.org/math/algebra/polynomials/multiplying_polynomials/v/multiplyingbinomials
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