Find the value of `a` and `b.`
`{5+sqrt 3}/{5-sqrt 3} =a+b sqrt 3`

Find the value of a and b if (i)(sqrt(3)+1)/(sqrt(3)-1)=a+bsqrt(3)" "(ii)(5+2sqrt(3))/(5-2sqrt(3))=a+bsqrt(3)

(i) If x = (6ab)/(a + b) , find the value of : (x + 3a)/(x - 3a) + (x + 3b)/(x - 3b) . (ii) a = (4sqrt(6))/(sqrt(2) + sqrt(3)) , find the value of : (a + 2sqrt(2))/(a - 2sqrt(2)) + (a + 2sqrt(3))/(a - 2sqrt(3)) .

Find the value of m and n : if : ( 5+ 2sqrt3)/( 7+ 4sqrt3) = m + n sqrt3

Find the values of a and b if : (2sqrt(3)+3sqrt(2))/(2sqrt(3)-3sqrt(2))=a+bsqrt(6)

Find the values of a and b in each of the (3)/(sqrt(3)-sqrt(2))= a sqrt(3)-bsqrt(2)

Find the values of a and b in each of the (2+sqrt(3))/(2-sqrt(3))= a+ bsqrt(3)

Find the values of a and b in each of the (5+3sqrt(2))/(5-3sqrt(2))= a+b sqrt(2)

Find the value of 6/(sqrt(5)-\ sqrt(3)) , it being given that sqrt(3)=1. 732\ \ a n d\ \ sqrt(5)=2. 236

Find (sqrt 3 - sqrt 5)(sqrt 5+ sqrt3)

Find the value of the "determinant" |{:(sqrt13+sqrt3,2sqrt5,sqrt5),(sqrt26+sqrt15,5,sqrt10),(sqrt65+3,sqrt15,5):}|