Question 181310
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I think you mean:


*[tex \LARGE \text{          }\math \frac {sqrt{7x}}{sqrt{3}}]


Rationalize the denominator means to take whatever action required so that the denominator of the fraction is a rational number.  In this case, multiplication of the denominator by *[tex \Large sqrt{3}] will do the trick nicely.  However, you can't just multiply the denominator by something other than 1 and still have the same value for the fraction overall.  The only thing you can multiply the whole fraction by is something that has a value of 1.  In this case, it will be convenient to multiply the entire fraction by *[tex \Large \frac {sqrt{3}}{sqrt{3}}], thus:


*[tex \LARGE \text{          }\math \left(\frac {sqrt{7x}}{sqrt{3}}\right)\left(\frac {sqrt{3}}{sqrt{3}}\right)= \frac {sqrt{21x}}{3}]


Your second problem is trivial because both of the radicands are perfect squares, meaning the square roots are rational.




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