(iv) Expand :-`(4+sqrt(-3))/(4-sqrt(-3))`

If sqrt(2)= 1.4 and sqrt(3) = 1.7 find the value of each of the correct to one decimal place: (2-sqrt(3))/(sqrt(3))

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

A line passes through point P(4,5) and makes 30^@ with X-axis. Then the coordinates of the point which is at distance of 4 unit on either side of P is : a. (4-2sqrt(3),7) , (4+2sqrt(3),7) b. (4+2sqrt(3),7) , (4-2sqrt(3),7) c. (4+2sqrt(3),7) , (4-2sqrt(3),3) d. (4-2sqrt(3),7) , (4-2sqrt(3),7)

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

Find the angle between the lines whose direction cosines are (-(sqrt3)/(4), (1)/(4), -(sqrt3)/(2)) and (-(sqrt3)/(4), (1)/(4), (sqrt3)/(2)) .

If A,B,C are the angles of a given triangle ABC . If cosA.cosB.cosC= (sqrt3-1)/8 and sinA.sinB.sinC= (3+sqrt3)/8 The cubic equation whose roots are tanA, tanB, tanC is (A) x^3-(3+2sqrt(3))x^2+(5+4sqrt(3))x-(3+2sqrt(3))=0 (B) x^3-(3+-2sqrt(3))x^2+(5+4sqrt(3))x+(3+2sqrt(3))=0 (C) x^3+(3+2sqrt(3))x^2+(5+4sqrt(3))x+(3+2sqrt(3))=0 (D) x^3-(3+2sqrt(3))x^2+(5+4sqrt(3))x+(3+2sqrt(3))=0

The value of cos^(-1)(cos(2tan^(-1)((sqrt(3)+1)/(sqrt(4-2sqrt(3)))))) is

The straight line 3x+4y-12=0 meets the coordinate axes at Aa n dB . An equilateral triangle A B C is constructed. The possible coordinates of vertex C (a) (2(1-(3sqrt(3))/4),3/2(1-4/(sqrt(3)))) (b) (-2(1+sqrt(3)),3/2(1-sqrt(3))) (c) (2(1+sqrt(3)),3/2(1+sqrt(3))) (d) (2(1+(3sqrt(3))/4),3/2(1+4/(sqrt(3))))

Express each one of the following with rational denominator: (i) (sqrt(3)+\ 1)/(2sqrt(2)-\ sqrt(3)) (ii) (6-4sqrt(2))/(6+4sqrt(2))