`(sqrt(6+2sqrt(5)))(sqrt(6-2sqrt(5)))`

Rationalize the denominatiors of : (sqrt(6)-sqrt(5))/(sqrt(6)+sqrt(5))

Simplify: (2sqrt(3)+sqrt(5))(2sqrt(3)-sqrt(5))

Simplify sqrt(5+2sqrt(6))+sqrt(8-2sqrt(15))

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

Rationalies the denominator and simplify: (i) (1+sqrt(2))/(3-2sqrt(2)) (ii) (2sqrt(6)-\ sqrt(5))/(3sqrt(5)-\ 2sqrt(6))

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)

Show that: 1/(3-sqrt(8))-1/(sqrt(8)-sqrt(7))+1/(sqrt(7)-sqrt(6))-1/(sqrt(6)-sqrt(5))+1/(sqrt(5)-2)=5

Find (x+a)^(5)+(x-a)^(5) . Hence, evaluate (sqrt(6)+sqrt(7))^(5)+(sqrt(6)-sqrt(7))^(5)

The centroid of an equilateral triangle is (0, 0). If two vertices of the triangle lie on x+y=2sqrt(2), then one of them will have its coordinates. (a) (sqrt(2)+sqrt(6),sqrt(2)-sqrt(6)) (b) (sqrt(2)+sqrt(3),sqrt(2)-sqrt(3)) (c) (sqrt(2)+sqrt(5),sqrt(2)-sqrt(5)) (d) none of these