SOLUTION: Hi, Please help me to solve step-by-step on these questions. Thank you very much. 14. a) What is the conjugate of the expression : √3 + √5 b) Multiply : &#

Algebra ->  Linear-equations -> SOLUTION: Hi, Please help me to solve step-by-step on these questions. Thank you very much. 14. a) What is the conjugate of the expression : √3 + √5 b) Multiply : &#      Log On


   

Question 1112825: Hi,
Please help me to solve step-by-step on these questions.
Thank you very much.
14.
a)
What is the conjugate of the expression :
√3 + √5
b)
Multiply :
√3 + √5
by its conjugate from part a.
Rationalize the denominator as shown in Section 8.5 for the following rational expression :
(2√(5-1))/(√(3 )+√5)

Found 3 solutions by Alan3354, solver91311, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a)
What is the conjugate of the expression :
√3 + √5
You have to know that. If you don't, look it up and remember it.
================
b)
Multiply :
√3 + √5
by its conjugate from part a.
Do that.
====================
Rationalize the denominator as shown in Section 8.5 for the following rational expression :
(2√(5-1))/(√(3 )+√5)
Not legible.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The conjugate of any binomial expression is created by changing the sign between the two terms, that is the conjugate of is

The product of any pair of conjugates is the square of the first term minus the square of the second term. E.g.

To rationalize a binomial denominator, multiply the entire fraction by 1 in the form of the conjugate of the denominator divided by itself.

Thus:



And then combine any like terms.

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
a)  What is the conjugate of the expression  sqrt%283%29+%2B+sqrt%285%29 ? 

                Conjugate of the expression  sqrt%283%29+%2B+sqrt%285%29  is  sqrt%283%29+-+sqrt%285%29

 

b)  Multiply  sqrt%283%29+%2B+sqrt%285%29  by its conjugate from part a.

              %28sqrt%283%29+%2B+sqrt%285%29%29%2A%28sqrt%283%29+-+sqrt%285%29%29 = 

                        use the formula  (a+b)(a-b) = a%5E2+-+b%5E2 

           =  %28sqrt%283%29%29%5E2+-+%28sqrt%285%29%29%5E2 = 3 - 5 = -2.


c)  Rationalize the denominator as shown in Section 8.5 for the following rational expression :
	(2√(5-1))/(√(3 )+√5)


           I can not read your formula adequately, since it was written carelessly . . . 

           Use parentheses properly.