Question

Rationalise. 1 divided by(√6-√11+√5)

Answer 1

1 (sqrt6 +(sqrt11 +sqrt5))
-------------------------------- = ------------------------------------------------------------------- =
(sqrt6 -(sqrt11 +sqrt5)) (sqrt6 -(sqrt11 +sqrt5)) *(sqrt6 +(sqrt11 +sqrt5))


(sqrt6 +(sqrt11 +sqrt5)) sqrt6 +sqrt11 + sqrt5
= ------------------------------------- = ------------------------------------------ =
6 -(sqrt11 +sqrt5)^2 (6 -(11 +2sqrt11 *sqrt5 +5)

sqrt6 +sqrt11 +sqrt5 (sqrt6 +sqrt11 +sqrt5)(10 -2sqrt55)
= --------------------------------- = - -------------------------------------------------- =
- 10 - 2sqrt55 (10 +2sqrt55)(10 -2sqrt55)


(sqrt6 +sqrt11 +sqrt5)(10 -2sqrt55)
= - --------------------------------------------------- =
100 -4*55

(sqrt6 +sqrt11 +sqrt5)(10-2sqrt55)
= - ------------------------------------------------------ =
100 -220

(sqrt6 +sqrt11 +sqrt5)(10-2sqrt55)
= - ---------------------------------------------------- =
- 120

(sqrt6 +sqrt11 +sqrt5)(10-2sqrt55)
= -----------------------------------------------------
120

hope this will help you

Answer 2

1/(√6-√11+√5)=1 / [(√6+√5) -(√11)]

1 / [(√6+√5) -(√11)]=[1 / [(√6+√5) -(√11)]*[(√6+√5) +(√11)] / [(√6+√5)+(√11)]=
=(√6+√5+√11) / [(6+2√30+5) - 11]=
=(√6+√5+√11) / 2√30=
=(√6+√5+√11)*(2√30) / (2√30*2√30)=
=(√6+√5+√11)*2√30 / 120=
=(√6+√5+√11)*√30/ 60=
=(√180+√150+√330) / 60

Answer:1/(√6-√11+√5)= (√180+√150+√330) / 60

To check:
1/(√6-√11+√5)=0.7304959....

(√180+√150+√330) / 60=0.7304959...