SOLUTION: I know I have to rationalize the denominator, im just not sure how it works with a square root and real number. Help, please! Thanks, Elizabeth. 11 ------- √7 + 8 a

Algebra ->  Radicals -> SOLUTION: I know I have to rationalize the denominator, im just not sure how it works with a square root and real number. Help, please! Thanks, Elizabeth. 11 ------- √7 + 8 a      Log On


   



Question 163585: I know I have to rationalize the denominator, im just not sure how it works with a square root and real number. Help, please! Thanks, Elizabeth.
11
-------
√7 + 8
and
3
--------
2√5 - √7

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I know I have to rationalize the denominator, im just not sure how it works with a square root and real number. Help, please! Thanks, Elizabeth.
11
-------
√7 + 8
//////////////////
Use the "conjugate" to get rid of radicals in the DEN. Multiply NUM and DEN by sqrt%287%29-+8
[11*(sqrt(7) -8]/(7 - 64)
= -%2811%2Asqrt%287%29+-+8%29%2F57
Multiplying by the "conjugate" is something you'll see more of to deal with radicals and imaginaries.
and
3
--------
2√5 - √7
----------------
Same approach, multiply by 2sqrt%285%29+%2B+sqrt%287%29
= 3%2A%282sqrt%285%29+%2B+sqrt%287%29%29%2F%2820+-+7%29
= %286sqrt%285%29+%2B+3sqrt%287%29%29%2F13