Evaluating the square root of $a^3/(1-a) + a+ a^2+1$

Question

How can we find the answer for this by solving without actually calculating.... $$\sqrt{\frac{(0.75)^3} {1 - (0.75) }+{(0.75 + (0.75)^2 + 1)}}$$

Actually I meant for the first square-root sign to strech over it all but I couldn't get it such so please understand that the WHOLE expression(including that brackets after that plus sign) is under that square-root..

Answer 1

By any chance, the whole expression is inside the sqrt, then use $\displaystyle1-a^3=(1-a)(1+a+a^2)$

Then we are left with $$\sqrt{\frac1{(1-0.75)}}=\sqrt{\frac1{(0.25)}}=\sqrt{\frac{100}{25}}=\cdots$$