sqrt((5)/(1)+4sqrt(-3))

3sqrt(48)-(5)/(2)sqrt((1)/(3))+4sqrt(3)

Rationales the denominator and simplify: (sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) (ii) (5+2sqrt(3))/(7+4sqrt(3)) (iii) (1+sqrt(2))/(3-2sqrt(2)) (2sqrt(6)-sqrt(5))/(3sqrt(5)-2sqrt(6)) (v) (4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18)) (vi) (2sqrt(3)-sqrt(5))/(2sqrt(3)+3sqrt(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))

If both a and b are rational numbers,find the values of a and b in each of the following equalities :(sqrt(3)-1)/(sqrt(3)+1)=a+b sqrt(3)( ii) (3+sqrt(7))/(3-sqrt(7))=a+b sqrt(7)(5+2sqrt(3))/(7+4sqrt(3))=a+b sqrt(3)( iv) (5+sqrt(3))/(7-sqrt(3))=47a+sqrt(3)b(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))=a+b sqrt(15) (iv) (sqrt(2)+sqrt(3))/(3sqrt(2)-2sqrt(3))=1-b sqrt(3)

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)

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

Find the value of a and b in each of the following (i)(3+sqrt(2))/(3-sqrt(2))=a+bsqrt(2)" "(ii)(sqrt(2)+1)/(sqrt(2)-1)=a-bsqrt(2)" "(iii)(5+4sqrt(3))/(5-4sqrt(3))=a-bsqrt(3)

Find the value of a and b in each of the following (i)(3+sqrt(2))/(3-sqrt(2))=a+bsqrt(2)" "(ii)(sqrt(2)+1)/(sqrt(2)-1)=a-bsqrt(2)" "(iii)(5+4sqrt(3))/(5-4sqrt(3))=a-bsqrt(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))

Rationales the denominator and simplify: (sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))( ii) (5+2sqrt(3))/(7+4sqrt(3))