List of top Quantitative Aptitude Questions on Surds and Indices asked in NPAT

The value of \[ \sqrt{1 + \frac{\sqrt{3}}{2}} - \sqrt{1 - \frac{\sqrt{3}}{2}} \text{ is:} \]
If \[ \frac{\sqrt{11} - \sqrt{120}}{\sqrt{11} + 6\sqrt{2}} = A\sqrt{6} + B\sqrt{5} + C\sqrt{3} + D\sqrt{10}, \text{ then the value of } (A + B + C + D) \text{ is:} \]
Let \[ x = \sqrt{-4\sqrt{2} + 17 (-\sqrt{2})^2 + 2}. \] If \( x = a + b \sqrt{2} \), then what is the value of \( (a - b) \)?
Let \[ x = \sqrt{-4\sqrt{2} + 17 (-\sqrt{2})^2 + 2}. \] If \( x = a + b \sqrt{2} \), then what is the value of \( (a - b) \)?
The sum of the roots of the equation \( |x - 7|^2 + 2|x| - 7| = 24 \) is: