3sqrt(147)-(7)/(3)sqrt((1)/(3))+7sqrt((1)/(3))

Simplify : 7sqrt((1)/(3)) -2(1)/(3) sqrt((1)/(3)) +3 sqrt( 147)

(3+sqrt(7))/(3-sqrt(7))

Simplify. (4)/(7)sqrt(147)+(3)/(8)sqrt(192)-(1)/(5)sqrt(75)

(7+3sqrt(5))/(3+sqrt(5))+(7-3sqrt(5))/(3-sqrt(5))

Simplify: (7+3sqrt(5))/(3+sqrt(5))-(7-3sqrt(5))/(3-sqrt(5)) (ii) (1)/(2+sqrt(3))+(2)/(sqrt(5)-sqrt(3))+(1)/(2-sqrt(5))

The number (7+5sqrt(2))^((1)/(3))+(7-5sqrt(2))^((1)/(3)) ,is equal to

(3 + sqrt7)(3 - sqrt7)

Find the direction cosines of the line which is perpendicular to the lines with direction ratios 4, 1, 3 and 2, -3, 1 . a) (1)/(sqrt(3)),(1)/(5sqrt(3)),(-7)/(5sqrt(3)) b) (5)/(sqrt(3)),(1)/(sqrt(3)),(7)/(5) c) (2)/(sqrt(3)),(5)/(2sqrt(3)),(1)/(7sqrt(3)) d) (1)/(sqrt(3)),(2)/(sqrt(3)),(-1)/(sqrt(3))

sqrt(2)+sqrt(3)+sqrt(7)-(1)/(sqrt(2)+sqrt(3)+sqrt(7))=?