`x= frac{sqrt 5-1}{sqrt 5 +1}`

frac{1}{sqrt7-4} frac{1}{sqrt11-7}

solve the equations: frac{2}{sqrt x} + frac{3}{sqrt y} =2 and frac{4}{sqrt x} - frac{9}{sqrt y} =-1

lim_(xrarr0) frac{sqrt(1+ x} -1}{x}

If x= ( sqrt5- sqrt3)/ ( sqrt5+ sqrt3) and y= ( sqrt5+ sqrt3)/( sqrt5- sqrt3) find the value of x^(2) + y ^(2)

Using properties of proportion, solve for x : (i) (sqrt(x + 5) + sqrt(x - 16))/ (sqrt(x + 5) - sqrt(x - 16)) = (7)/(3) (ii) (sqrt(x + 1) + sqrt(x - 1))/ (sqrt(x + 1) - sqrt(x - 1)) = (4x -1)/(2) . (iii) (3x + sqrt(9x^(2) -5))/(3x - sqrt(9x^(2) -5)) = 5 .

If 4^x-\ 4^(x-1)=24 , then (2x)^x equals (a) 5sqrt(5) (b) sqrt(5) (c) 25sqrt(5) (d) 125

If two zeros of x^3+x^2-5x-5 are sqrt(5) and -sqrt(5) , then its third zero is (a) 1 (b) -1 (c) 2 (d) -2

Rationalize the denominator 1/(sqrt 3 - sqrt 2) - 2/(sqrt 5 - sqrt 3) + 3/(sqrt 5 - sqrt 2)

Find the range of f(x)sqrt(x-1)+sqrt(5-1)

Find the range of f(x) = sqrt(x-1)+sqrt(5-x)