<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-rationalizing-denominators">Rationalizing Denominators Exercise</a></p><p>For some reason, it <strong><u>really</u></strong> 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're <u><strong>not changing</strong></u> the fraction's value here because we'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 "opposite." 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>