`(sqrt(4^(5))times sqrt(4^(-3)))/(sqrt(4^(-2)))=`

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

3sqrt(2^(5))sqrt(4^(9))sqrt(8)=

(4+sqrt(2))/(2+sqrt(2))times(2-sqrt(2))/(2-sqrt(2))

Which of the following is equal to root(3)(-1) a. (sqrt(3)+sqrt(-1))/2 b. (-sqrt(3)+sqrt(-1))/(sqrt(-4)) c. (sqrt(3)-sqrt(-1))/(sqrt(-4)) d. -sqrt(-1)

Simplify :- (i) (6)/(sqrt(2)) (ii) (sqrt(3))/(3) (iii) sqrt((3)/(4)) (iv) (6)/(sqrt(2)) (v) (sqrt(5))/(10) (vi) sqrt((16)/(2))

Using componendo and dividendo, find the value of x if (sqrt(3x+4)+sqrt(3x-5))/(sqrt(3x+4)-sqrt(3x-5))=9 .

The direction ratios of the line 2y+z-5=0=x-3y-6 are proportional to 3,\ 1,\ -2 b. 2,\ -4,\ 1 c. 3/(sqrt(14)),1/(sqrt(14)),(-2)/(sqrt(14)) d. 2/(sqrt(41)),(-4)/(sqrt(41)),1/(sqrt(41))

Simplify: (4+\ sqrt(5))/(4-sqrt(5))+(4-\ sqrt(5))/(4+\ sqrt(5))

sin( 67 1/2)^(@) + cos( 67 1/2)^(@) is equal to A) 1/2sqrt(4+2sqrt(2)) , B) 1/2sqrt(4-2sqrt(2)) , C) 1/4(sqrt(4+2sqrt(2))) , D) 1/4(sqrt(4-2sqrt(2)))

Simplify each of the following by removing radical signs and negative indices wherever they occur: (i)\ (sqrt(4))^(-3/4) (ii)\ (sqrt(5))^(-3)\ xx\ (sqrt(2))^(-3) (iii)1/(4^(-5)3)