rationalize the denominator

Question

Rationalize the denominator.

8/5-(squareroot)6= ___.

Simplify your answer.

 

 

help is appreciated, thank you!

 

 

 

Answer 1

To rationalize the denominator of 8/(5-√6), multiply the numerator and denominator by 5 + √6.

 

Doing this, we get 8(5+√6)/[(5-√6)(5+√6)] = 8(5+√6)/19

 

                      

Answer 2

Dear Laura,

    Here are some steps to follow:

 

Look at your denominator, and use the radical.  Multiply bottom and top by it, which is the same as multiplying by "1."

 

 

     8/5√(6)   = 8      *  √(6) =  8 √(6)    = 8 √(6) = 8√(6) =                              Rename 8/30 in lowest terms.

                      5√(6) * √(6)     5* √36)     5*6        30                                      You can divide bottom and top

                                                                                                                         by "2."

 

                    

                    8√(6) =  4√(6)        Answer           Note:  √(a)*  √(a) = a, so  √(6) * √(6) = 6 ,  and √(36) = 6

                              30          15

 

 

I hope that this problem helps. 

                                                                       Thank you,

                                                                         Susan C.