`(3+sqrt(5))/(3-sqrt(5))`

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))

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))

If a+bsqrt(5)=(4-3sqrt(5))/(4+3sqrt(5)) , then find the values of a and b.

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)

In each of the following determine rational number a\ a n d\ b : (i)\ (sqrt(11)-sqrt(7))/(sqrt(11)+\ sqrt(7))=a-bsqrt(77) (ii)\ (4+3sqrt(5))/(4-3sqrt(5))=a+bsqrt(5)

Simplify each of the following : (i) 3/(5-sqrt(3))+2/(5+sqrt(3)) (ii) (4+sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (iii) (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+2)/(sqrt(5)-2)

Solve : (4-sqrt(5))/(4+sqrt(5))+ (2)/(5+sqrt(3))+(4+sqrt(5))/(4-sqrt(5))

Express the following in the form a+bi, where a and b are real numbers ((3 + sqrt5i) (3-sqrt5i))/((sqrt3+sqrt2i)- (sqrt3-sqrt2i))

Find the values of each of the following correct to three places of decimals, it being given that sqrt(2)=1. 4142 ,\ sqrt(3)=1. 732 ,\ \ sqrt(5)=2. 2360 ,\ sqrt(6)=2. 4495 and sqrt(10)=3. 162. (i)\ (3-sqrt(5))/(3+2sqrt(5)) (ii)\ (1+sqrt(2))/(3-2sqrt(2))

Simplify the following expressions: (i) (3+sqrt(3))\ (3-sqrt(3)) (ii) (sqrt(5)-\ sqrt(2)\ )(sqrt(5)+sqrt(2))