<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-roots">Roots Exercise</a></p><p>Beyond the four arithmetic operations mentioned earlier, there are other operations you need to know about.</p>
<p><span style="font-size:18px;"><strong>Roots</strong></span></p>
<ul>
<li><span style="color:#8e44ad;">Other Names</span>
<ul>
<li>We don't say "find the second root" of something. We say "take the square root."</li>
<li>We don't say "find the third root" of something. We say "take the cube root."</li>
<li>For everything else, we simply say $4$th root, $5$th root, etc.</li>
</ul>
</li>
</ul>
<p>So what are roots? Essentially they are the <span style="color:#27ae60;">REVERSE </span>of exponents. They undo the exponent process. See the examples below:</p>
<p style="text-align: center;">$4^2=16$ and $\sqrt{16}=4$</p>
<p style="text-align: center;">$3^3=27$ and $\sqrt[3]{27}=3$</p>
<p style="text-align: center;">$-3^3=-27$ and $\sqrt[3]{-27}=-3$</p>
<p><span style="font-size:18px;"><strong>Several Important Points</strong></span></p>
<ol>
<li>"Even" roots, like the square root, the $4$th root, the $6$th root, etc. can <span style="color:#e74c3c;">ONLY </span>take positive values or zero. No negatives allowed. $\sqrt{-25}$ makes no dang sense.</li>
<li>"Odd" roots, like the cube root, the $5$th root, the $7$th root, etc. can take positive <span style="color:#e74c3c;">OR</span> negative values (or zero). Everything is allowed. $\sqrt[3]{27}$ and $\sqrt[3]{-27}$ both make sense.</li>
<li>If $n^2=64$, then $n$ equals <span style="color:#e74c3c;">BOTH</span> $8$ and $-8$.</li>
<li>However, if we take $\sqrt{64}$, the result is <span style="color:#e74c3c;">ONLY</span> $8$. (You might have been taught differently in your school. This is how ETS likes to do it.)</li>
</ol>