Answer
$a.) \ \vert \vert u \vert \vert = \dfrac{\sqrt{17}}{4}$
$b.) \ \vert \vert v \vert \vert = \dfrac{5\sqrt{41}}{8}$
$c.) \ \vert\vert u+v\vert\vert = \dfrac{\sqrt{577}}{8}$
Work Step by Step
Given $u =(-1,\frac{1}{4})$ and $v = (4,-\frac{1}{8})$
$a.) \ \vert \vert u \vert \vert = \sqrt{(-1)^2+(\frac{1}{4})^2} = \sqrt{1+\frac{1}{16}} = \sqrt{\frac{17}{16}} = \dfrac{\sqrt{17}}{4}$
$b.) \ \vert \vert v \vert \vert = \sqrt{(4)^2+(-\frac{1}{8})^2} = \sqrt{16+\frac{1}{64}} = \sqrt{\frac{1025}{64}} = \dfrac{5\sqrt{41}}{8}$
$c.) \ \vert\vert u+v\vert\vert = \sqrt{(-1+4)^2+(\frac{1}{4}-\frac{1}{8})^2} = \sqrt{(3)^2+(\frac{1}{8})^2}=\sqrt{9+\frac{1}{64}}=\sqrt{\frac{577}{64}}=\dfrac{\sqrt{577}}{8}$
