Question

How do you find all real square roots of -9/16

Answer 1

well, the value is negative, thus any EVEN root will yield no "real" roots, just imaginary ones

Answer 2

\(\bf {\color{blue}{ 9=3^2\qquad 16=14^2}}\\ \quad \\ \quad \\
\pm\sqrt{-\cfrac{9}{16}}\implies \pm\sqrt{-1\cdot \cfrac{9}{16}}\implies \pm\sqrt{\cfrac{9}{16}}\cdot \sqrt{-1}\implies \pm \sqrt{\cfrac{3^2}{4^2}}\ i\\\quad\\\implies \pm\cfrac{3}{4}\ i\)