Question

Find the square root of
$\frac{3}{2}(x-1)+\sqrt{2x^3-7x-4}$

Answer 1

The expression

$\frac{3}{2}(x-1)+\sqrt{2x^3-7x-4}$

$=\frac{1}{2}[3x-3+2\sqrt{(2x+1)(x-4)}]$
$=\frac{1}{2}\left[\right(2x+1)+(x-4)+2\sqrt{(2x+1)(x-4)}]$
hence, by inspection, the square root is
$=\frac{1}{\sqrt{2}}(\sqrt{2x+1}+\sqrt{x-4})$