Question 1037704
<font face="Times New Roman" size="+2">


I don't know how to "slove"[sic] these kinds of problems either.  I don't know how to "slove" any kind of problem.  I know how to <i>solve</i> problems where you have a mathematical expression that contains a relational operator, but that is not the case here.  Therefore, solve, despite the fact that it is actually an English word, is not the correct word.  However, I think I can help you answer this question.


An expression such as *[tex \Large \sqrt{t}] can be simplified if the prime factorization of *[tex \Large t] contains any pairs of prime factors.


Note that *[tex \Large 21x] has 3 factors, namely *[tex \Large 3], *[tex \Large 7], and *[tex \Large x].  If *[tex \Large x] were replaced by *[tex \Large 5] or *[tex \Large 37], both of which are prime and neither of which pairs either of the two factors of *[tex \Large 21], then there is no simplification that can be done.  However, the same cannot be said of the other two choices.  This problem has two correct answers, b and d.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{21\cdot8}\ =\ \sqrt{2\cdot2\cdot2\cdot3\cdot7}\ =\ 2\sqrt{42}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{21\cdot54}\ =\ \sqrt{2\cdot3\cdot3\cdot3\cdot3\cdot7}\ =\ 9\sqrt{14}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

</font>