Question 219094
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Derive the prime factorization of the radicand.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\ \times\ 3\ \times\ 3\ =\ 18]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{18} = \sqrt{2\ \times\ 3\ \times\ 3}\ = \ \sqrt{2}\ \cdot\ \sqrt{3\ \times\ 3}]


Because:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \forall\ a,\,b\ \geq\ 0, \sqrt{ab}\ =\ \sqrt{a}\ \cdot\ \sqrt{b}]


But


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{3\ \times\ 3} = 3]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{18} = 3\ \cdot\ \sqrt{2}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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