Question

rationalize 1/√5-√6+√11

Answer 1

1 / (  √5 +  √6 -  √11) * (  √5 +  √6 + √ 11) / ( √5 + √6 +  √11)

= (√5 + √6 + √11) / (√5 + √6)2 - (√11)2

(√5 + √6 + √11) / (11 + 2√30 - 11)

(√5 + √6  + √11 ) / (2√30)

(√5 + √6 +√11)/ (2√30) * (2√30) / (2√30)

(2√150 + 2√180 + 2√330) / 4 * 30

2(√150 + √180 + √330) / 4 * 30

(√150 + √180 + √330) / 60

(5√6 + 6√5 + √330) / 60
and the answer is
answer =1.3143486431