Rationalizing Denominators

<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-rationalizing-denominators">Rationalizing Denominators Exercise</a></p><p>For some reason, it&nbsp;<strong><u>really</u></strong>&nbsp;bothers mathematicians when there is a radical in the denominator of a fraction. To get rid of it, we need to <strong><span style="color:#27ae60;">Rationalize the Denominator</span></strong>.</p> <ul> <li>If there is a single radical in the denominator of a fraction, multiply both the numerator and denominator by that radical. This will have the effect of removing the radical from the denominator.</li> </ul> <p>$$\frac{2}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{2\sqrt{3}}{3}$$</p> <p>Notice how we&#39;re <u><strong>not changing</strong></u> the fraction&#39;s value here because we&#39;re essentially multiplying it by $1$.</p> <ul> <li>If there is a radical and something else in the denominator of the fraction, multiply both the numerator and the denominator by its conjugate -- basically its &quot;opposite.&quot; See the example below:</li> </ul> <p>$$\frac{3}{\sqrt{3}+2} \times \frac{\sqrt{3}-2}{\sqrt{3}-2} = \frac{3\sqrt{3}-6}{3-4}= \frac{3\sqrt{3}-6}{-1}$$</p>