" (iii) "(2sqrt(13))/(3sqrt(52)-4sqrt(117))

If G is the centroid of triangle ABC and BC=3,CA=4 AB=5 then BG= (sqrt(13))/(3) (2sqrt(13))/(3) sqrt(13) (4sqrt(13))/(3)

Rationales the denominator and simplify: (4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18))( ii) (2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))

Let z_(1)=(2sqrt(3)+ i6sqrt(7))/(6sqrt(7)+ i2sqrt(3))" and "z_(2)=(sqrt(11)+ i3sqrt(13))/(3sqrt(13)- isqrt(11)) . Then |(1)/(z_1)+(1)/(z_2)| is equal to

sin[(1)/(2)cot^(-1)((2)/(3))]= sqrt((sqrt(13)-2)/(2sqrt(13))) (2+sqrt(13))/(2sqrt(13)) sqrt((2-sqrt(13))/(2sqrt(13))) (2-sqrt(13))/(2sqrt(13))

(3sqrt(2))/(sqrt(6)-sqrt(3))+(2sqrt(3))/(sqrt(6)+2)-(4sqrt(3))/(sqrt(6)-sqrt(2))

Simplify (sqrt(13)-sqrt(11))/(sqrt(13)+sqrt(11)) + (sqrt(13)+sqrt(11))/(sqrt(13)-sqrt(11))

If a=(4sqrt(6))/(sqrt(2)+sqrt(3))

If both a and b are rational numbers,find the values of a and b in each of the following equalities :(sqrt(3)-1)/(sqrt(3)+1)=a+b sqrt(3)( ii) (3+sqrt(7))/(3-sqrt(7))=a+b sqrt(7)(5+2sqrt(3))/(7+4sqrt(3))=a+b sqrt(3)( iv) (5+sqrt(3))/(7-sqrt(3))=47a+sqrt(3)b(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))=a+b sqrt(15) (iv) (sqrt(2)+sqrt(3))/(3sqrt(2)-2sqrt(3))=1-b sqrt(3)

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

(3sqrt(2)-sqrt(3))(4sqrt(3)-sqrt(2))