" 12."5sqrt(3)+2sqrt(27)-(1)/(sqrt(3))

7sqrt(3)+2sqrt(27)

Simplify: 5sqrt(3)+2sqrt(27)+1/(sqrt(3))

Simplify : 5sqrt(3)+2sqrt(27)+1/sqrt(3)

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))

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

Simplify: (i) (3sqrt(2)-2sqrt(2))/(3sqrt(2)+\ 2sqrt(3))+(sqrt(12))/(sqrt(3)-\ sqrt(2)) (ii) (sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3))+(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3))

(sqrt(12)+sqrt(5)+sqrt(3))/(sqrt(12)-sqrt(5)-sqrt(3))+(sqrt(20)+sqrt(5)+sqrt(3))/(sqrt(20)-sqrt(5)-sqrt(3))

Given that sqrt(3) = 1.732, the value of (3 + sqrt(6 ))/( 5 sqrt(3) - 2 sqrt(12) - sqrt(32) + sqrt(50)) is