SOLUTION: Hello there, I am currently working on an optional summer packet for school, and I came across this problem. I have the answer available to me, but I don't understand how to get t

Algebra ->  Radicals -> SOLUTION: Hello there, I am currently working on an optional summer packet for school, and I came across this problem. I have the answer available to me, but I don't understand how to get t      Log On


   

Question 149989: Hello there,
I am currently working on an optional summer packet for school, and I came across this problem. I have the answer available to me, but I don't understand how to get the answer. If you could explain to me how to simplify this expression, I'd greatly appreciate it.
(2)/(5 - +sqrt%28+3+%29+)
Thank you!
Found 2 solutions by scott8148, nerdybill:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the radical in the denominator is a no-no
__ so it is removed by multiplying the numerator and denominator by 5+sqrt(3), the conjugate of the denominator

2[5+sqrt(3)]/[(5-sqrt(3))*(5+sqrt(3))] __ [10+2sqrt(3)]/[5^2-(sqrt(3))^2] __ [10+2sqrt(3)]/(25-3)

[5+sqrt(3)]/11

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
The idea here, is to get rid of the square root sign from the denominator.
.
Starting with:
(2)/(5 - +sqrt%28+3+%29+)
Multiply numerator and denominator by (5 + +sqrt%28+3+%29+)
.
(2)/(5 - +sqrt%28+3+%29+) * (5 + +sqrt%28+3+%29+)/(5 + +sqrt%28+3+%29+)
.
Resulting in:
2(5 + +sqrt%28+3+%29+)/ (25-3)
2(5 + +sqrt%28+3+%29+)/ (22)
(5 + +sqrt%28+3+%29+)/ 11