Simplify `sqrt(asqrt(asqrt(asqrt(a))))` for `a=3^(16/15)`

xsqrt(x)+ysqrt(y)=asqrt(a)

3/(sqrt3-sqrt2)=asqrt3-bsqrt2

If log_((sqrt(bsqrt(bsqrt(bsqrt(b)))))(sqrt(asqrt(asqrt(asqrt(asqrt(a))))))=x log_(b) a , then x =

For (1)/(asqrt(x)+bsqrt(y)) the rationalising factor is a asqrt(x)-bsqrt(y) . If x=(7sqrt(3))/(sqrt(10)+sqrt(3))-(3sqrt(2))/(sqrt(15)+3sqrt(2))-(2sqrt(5))/(sqrt(6)+sqrt(5)) , then value of x^(4)+x^(2) is

Let a and b be two positive real numbers such that at asqrt(a) + bsqrt(b) = 32 and asqrt(b) + bsqrt(a) = 31 . What is the value of (5(a+b))/7 ?

Suppose a, b are positive real numbers such that asqrt(a) + b sqrt(b) = 183, asqrt(b) + bsqrt(a) = 182 . Find 9/5(a-b) .

Remove the irrationality in the denominator a.sqrt((sqrt(2)-1)/(sqrt(2)+1)) b.(1)/(1+sqrt(2)+sqrt(3))

int_-a^asqrt((a-x)/(a+x))dx