If x is so small that x square and heigher power of x can be neglected , then approximate value of (1+3/4)1/2 (1-2x/3)-2 IS
The formula for the binomial expansion of
(1+ax)^n, where n is negative
is:
1+n(ax)+(n⋅(n−1)/2!)*(ax)^2...((n(n-1)...(n−r+1))/r!)(ax)^r.
As x^2 and higher powers can be neglected, (1+ax)^n = 1+n.ax
So, the given expression equates to ((7/4)^(1/2))*(1+4x/3) which is equal to (root(7)/2)*(1+4x/3).
Hope it helps.