Rationalize the numerator.
(sqrt19-(7))/(sqrt14+(7))

Question

Rationalize the numerator.
(sqrt19-(7))/(sqrt14+(7))

jhonyy9 · Answer

do you know what mean ,,rationalize" ?

jhonyy9 · Answer

so in this case the numerator ...
this is sure ? not the denominator ?

anonymous · Answer

No

anonymous · Answer

It is the numerator

jhonyy9 · Answer

ok 

so than you need rationalizing the numerator 

do you know what mean ,,rationalizing " ?

anonymous · Answer

No

jhonyy9 · Answer

so do you know that a^2 -b^2 = (a-b)(a+b)

yes ?

anonymous · Answer

And it is only sqrt19 and sqrt14 that is why I tried to separate them out. Hope I did it right.

anonymous · Answer

yes

jhonyy9 · Answer

so yes you have do it right 

than there are 

sqrt19  -7
---------- = 
sqrt14 +7

so because you know that a^2 -b^2 =(a-b)(a+b) 
and you need rationalizing the numerator what is in this case sqrt19  -7 so than you need to know that sqrt19  -7 has the conjugate sqrt19  +7 

yes ?

anonymous · Answer

yes

jhonyy9 · Answer

hopw that you see it now that if you multiplie the numerator by conjugate you will get for numerator

(sqrt19 -7)*sqrt(19 +7) = 19 -49 = -30 

but this is very important that you can multiplie the numerator by the conjugate just you will multiplie with this conjugate of numerator the denominator too 

so than you will  write 

(sqrt19  -7) *(sqrt19 +7)        19 -49
---------------------- = ------------
(sqrt14  +7) *(sqrt19 +7)      

can you ending the calcule ?

anonymous · Answer

no

anonymous · Answer

I am an idiot when it comes to math

jhonyy9 · Answer

ok 

so than for numerator there will be -30 ,yes ?

anonymous · Answer

yes

jhonyy9 · Answer

ok

and for denominator there are 

(sqrt14 +7) *(sqrt19 +7) = sqrt(14*19 +7sqrt14 +7sqrt19 +49 = sqrt266 + 7(sqrt14 +sqrt19) +49

so can you simplifie the sqrt266 ?

anonymous · Answer

would the answer be -30/sqrt266+7sqrt19+7sqrt14+49

jhonyy9 · Answer

yes but you see that from7sqrt19 and 7sqrt14 you can factorizing out the 7

anonymous · Answer

or -30/sqrt266+14sqrt19+49

jhonyy9 · Answer

how you have got 14sqrt19 ?

and where will be the sqrt14 ?

anonymous · Answer

that's why I think it is -30/sqrt266+7sqrt19+7sqrt14+49

jhonyy9 · Answer

so than this will be the right answer sure 

ok ?

than good luck

bye 


was my pleasure to help you

anonymous · Answer

thank you. What did you mean about factoring out 7

jhonyy9 · Answer

so than you will get 7sqrt19 +7sqrt14 = 7(sqrt19 +sqrt14)

anonymous · Answer

so i guess either would be ok

jhonyy9 · Answer

yes good luck

bye