SOLUTION: Please help me simplify this problem: square root of 8 divided by 2 times the square root of 5 plus the square root of six. Sorry, I do not know how to make a square root sign s

Algebra ->  Radicals -> SOLUTION: Please help me simplify this problem: square root of 8 divided by 2 times the square root of 5 plus the square root of six. Sorry, I do not know how to make a square root sign s      Log On


   

Question 31715: Please help me simplify this problem: square root of 8 divided by 2 times the square root of 5 plus the square root of six.
Sorry, I do not know how to make a square root sign so I could not type the problem out but I will type it out without the square root signs to give you some idea. The square root signs go over the 8, 5, and the six:
8%2F2%215%2B6
Ignore the ! (exclamation mark)
The six is supposed to be part of the denominator!
Thanks ahead of time for helping me!
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
+%28sqrt%288%29%29%2F%282%2A%28sqrt%285%29+%2B+sqrt%286%29%29%29+
First thing you MUST do is rationalize the denominator by multiplying by the conjugate +%28sqrt%285%29-+sqrt%286%29%29+


When multiplying by the conjugate, the roots cancel
+%28%28sqrt%288%29%29%28sqrt%285%29-sqrt%286%29%29%29%2F%282%285-6%29%29+
Multiply out the numerator
+%28sqrt%2840%29+-+sqrt%2848%29%29%2F%282%285-6%29%29+
Work out the roots
+%282%28sqrt%2810%29%29+-+2%28sqrt%283%29%29%29%2F%282%285-6%29%29+
Reduce all parts by 2
+%28sqrt%2810%29+-+sqrt%283%29%29%2F%285-6%29+
work the denominator
+%28sqrt%2810%29+-+sqrt%283%29%29%2F-1+
Some instructors will allow you to leave it in this form ... otherwise change the signs of the numerator and drop the denominator
+sqrt%283%29+-+sqrt%2810%29%29+