Question

Rationalize the denominator 1/ root 6 + root 5 - root 11

Answer 1

 I'm taking Under root = r
And Multiplication sign = X

    1/root 5+ root 6 - root 11 X ( r5 + r6 ) + r11 upon r5 + r6 + r11
  = r5 + r6 + r11 upon ( r5 + r6 ) square - (r11) square
  = r5 + r6 + r11 upon (r5)sq. + ( r6 )sq. + 2 X r5 X r6 X 11
  = r5 + r6 + r11 upon 5 + 6 + 2 root 30 - 11
  = r5 + r6 + r11 upon 2 root 30
  = r5 + r6 + r11 upon 2 root 30  X root 30 upon root 30
  = r150 + r180 + r330 upon 2 X 30 

  = 5root 6 + 6root 5 + root 30 upon 60     ans.

* If you will solve this question in notebook this answer would be much clear     to you.

Answer 2

Answer:

 = 5root 6 + 6root 5 + root 30 upon 60     ans.

Step-by-step explanation:

1/root 5+ root 6 - root 11 X ( r5 + r6 ) + r11 upon r5 + r6 + r11

 = r5 + r6 + r11 upon ( r5 + r6 ) square - (r11) square

 = r5 + r6 + r11 upon (r5)sq. + ( r6 )sq. + 2 X r5 X r6 X 11

 = r5 + r6 + r11 upon 5 + 6 + 2 root 30 - 11

 = r5 + r6 + r11 upon 2 root 30

 = r5 + r6 + r11 upon 2 root 30  X root 30 upon root 30

 = r150 + r180 + r330 upon 2 X 30  

 = 5root 6 + 6root 5 + root 30 upon 60     ans.

* If you will solve this question in notebook this answer would be much clear     to you.