Find the value of `a` and `b.`
`{4+sqrt 5}/{4-sqrt 5}=a+b sqrt 5`

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)

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

2sqrt5 - sqrt5 = sqrt5

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

(2) Find a and b if (5-sqrt6)/(5+sqrt6) =a+bsqrt 6

Find the value of sqrt((log_(0.5)4)^(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 the values of a and b in each of the following : (a)(5+2sqrt3)/(7+4sqrt(3))=a-6sqrt(3)" "(b)(3-sqrt(5))/(3+2sqrt(5))=asqrt(5)-(19)/(11) (c )(sqrt(2)+sqrt(3))/(3sqrt2-2sqrt(3))=2-bsqrt(6)" "(d)(7+sqrt(5))/(7-sqrt(5))-(7-sqrt(5))/(7+sqrt(5))=a+(7)/(11)sqrt(5b)

Rationalize the denominator and simplify to find the value of 4/(sqrt(5)+sqrt(3)) , given that sqrt(5)=2.236 and sqrt(3)=1.732