`sqrt5/(sqrt7-sqrt5)`

Simplify (7sqrt3)/(sqrt10+sqrt3)-(2sqrt5)/(sqrt6+sqrt5)-(3sqrt2)/(sqrt15+3sqrt2)

Rationlise the denominator and simplify: (sqrt5+sqrt3)/(sqrt5-sqrt3)

solve (3sqrt5 +sqrt3)/(sqrt5 -sqrt3)

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

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)

Simplify each of the following by rationalising the denominator; 1/(5+sqrt(2)) (ii) (5+sqrt(6))/(5-sqrt(6)) (iii) (7+3sqrt(5))/(7-3sqrt(5)) (iv) (2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))

(iii) (sqrt 5+ sqrt 3)/(sqrt5-sqrt3)+(sqrt5-sqrt3)/(sqrt5+sqrt3) =?

Simplify each of the following by rationalising the denominator: (7+3sqrt(5))/(7-3sqrt(5)) (ii) (2\ sqrt(3)-\ sqrt(5))/(2sqrt(2)+\ 3sqrt(3))

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

Simplify 5^(log1//5^((1//2)))+log_sqrt2(4/(sqrt7+sqrt3))+log_(1//2)(1/(10+2sqrt21)) .