Formulaic Maths Problems

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Let $\mathbf{v} = \begin{pmatrix} -6.7 \\ -2.2 \end{pmatrix}$. Find $|\mathbf{v}|$.

Hint: Square the components, add the results together, then take the square root.

$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A1}}\hspace{54px}}~} {}^2 + \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A2}}\hspace{54px}}~} {}^2$ $[-6.7] {}^2 + [-2.2] {}^2$

$= \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B1}}\hspace{54px}}~} + \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B2}}\hspace{54px}}~} = \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{BR}}\hspace{54px}}~}$ $= [44.89] + [4.84] = [49.73]$

Therefore,

$|\mathbf{v}| = \sqrt{\class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{C1}}\hspace{54px}}~}} = \class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{CR}}\hspace{54px}}~}$ $|\mathbf{v}| = \sqrt{[49.73]} = [7.05195008]$