Let's calculate: $\mathrm{norm}\left(\mathrm{coord}(5,12)\right)$

ⅰ $\mathrm{norm}\left(\mathrm{coord}(5,12)\right)$ = $\sqrt{5^2+{12}^2}$

$\sqrt{5^2+{12}^2}$

ⓘ Powers are computed before multiplications, additions and subtractions. With a positive integer exponent, a power corresponds to a repeated product: $5^2$ = $5\times 5$ = $25$■Calculate powers before multiplications, additions and subtractions. A power with a positive integer exponent is a repeated product: ${12}^2$ = $12\times 12$ = $144$

$\sqrt{25+144}$

ⓘ Start by calculating what is inside the parentheses: $25+144$ = $169$

$\sqrt{169}$

ⓘ The square root of a nonnegative real number is the nonnegative number whose square is that number: $\sqrt{169}$ = $13$ since ${13}^2$ = $169$

▶Result:   $13$