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- <title>Al Azhar 9th Grade Lesson Notes</title>
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- <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3>
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- <a href="/about/author.html" class="sidebar-link link">About the Author</a>
- <a href="/about/school.html" class="sidebar-link link">About School</a>
- <a href="/lessons" class="sidebar-link link">Lessons</a>
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- <h4>Table of Contents</h4>
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- <h1 class="banner-text" id="banner-txt">Root</h1>
- <h3 class="banner-text" id="banner-txt">Chapter 1</h3>
- </div>
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- <div class="chip-container" id="chip-container">
- <div class="chip"><span>✅ Verified</span></div>
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- <section>
- <h1 id="definition">Definition</h1>
- Root is the inverse of exponent. For example;<br>
- <ul>
- <li>4<sup>2</sup> = 16, <b>so <span class="sroot">16</span> = 4</b></li>
- <li>5<sup>2</sup> = 25, <b>so <span class="sroot">25</span> = 5</b></li>
- <li>10<sup>2</sup> = 100, <b>so <span class="sroot">100</span> = 10</b></li>
- </ul>
-
- <h1 id="simplification">Simplifying Square Roots</h1>
- You can simplify a root by factoring the root number another number that is rational. Or in other words, divide the root number by the perfect squares. For example;
- <ul>
- <li>
- <strong>Simplify <span class="sroot">60</span></strong><br>
- <span class="sroot">60</span> = <span class="sroot">4 &times; 15</span> = 2<span class="sroot">15</span><br>
- </li>
- <li>
- <strong>Simplify <span class="sroot">48</span></strong><br>
- <span class="sroot">48</span> = <span class="sroot">16 &times; 3</span> = 4<span class="sroot">3</span><br>
- </li>
- <li>
- <strong>Simplify <span class="sroot">125</span></strong><br>
- <span class="sroot">125</span> = <span class="sroot">25 &times; 5</span> = 5<span class="sroot">5</span><br>
- </li>
- </ul>
-
- <h1 id="root-operations">Root Operations</h1>
- <h2 id="root-operations--addition">Addition</h2>
- Roots with coefficient can be added with another coefficient that have the same roots. <br>
- <strong>a<span class="sroot">c</span> + b<span class="sroot">c</span> = (a + b)<span class="sroot">c</span></strong>
- <ul>
- <li>3<span class="sroot">2</span> + 4<span class="sroot">2</span> = (3 + 4)<span class="sroot">2</span> = <strong>7<span class="sroot">2</span></strong></li>
- <li><span class="sroot">5</span> + 3<span class="sroot">5</span> = (1 + 3)<span class="sroot">5</span> = <strong>4<span class="sroot">5</span></strong></li>
- </ul>
- <h2 id="root-operations--subtraction">Subtraction</h2>
- Roots with coefficient can be subtracted with another coefficient that have the same roots. <br>
- <strong>a<span class="sroot">c</span> - b<span class="sroot">c</span> = (a - b)<span class="sroot">c</span></strong>
- <ul>
- <li>7<span class="sroot">3</span> - 4<span class="sroot">3</span> = (7 - 4)<span class="sroot">3</span> = <strong>3<span class="sroot">2</span></strong></li>
- <li>10<span class="sroot">6</span> - 5<span class="sroot">6</span> = (10 - 5)<span class="sroot">6</span> = <strong>5<span class="sroot">6</span></strong></li>
- </ul>
- <h2 id="root-operations--multiplication">Multiplication</h2>
- Roots can be multiplied with any other roots. If the root is the same as the other multiplied root, the root can be deleted (if you want to be faster). <br>
- <strong>a<span class="sroot">c</span> &times; b<span class="sroot">d</span> = (a &times; b)<span class="sroot">c &times; d</span></strong>
- <ul>
- <li><span class="sroot">2</span> &times; <span class="sroot">5</span> = <strong><span class="sroot">10</span></strong></li>
- <li>3<span class="sroot">2</span> &times; 4<span class="sroot">3</span> = (3 &times; 4)<span class="sroot">2 &times; 3</span> = <strong>12<span class="sroot">6</span></strong></li>
- <li>2<span class="sroot">5</span> &times; 3<span class="sroot">5</span> = (2 &times; 3)(5) = 6(5) = <strong>30</strong></li>
- </ul>
- <h2 id="root-operations--division">Division</h2>
- Roots can be divided with any other roots. <br>
- <strong>a<span class="sroot">c</span> &divide; b<span class="sroot">d</span> = (a &divide; b)<span class="sroot">c &divide; d</span></strong>
- <ul>
- <li>
- 8<span class="sroot">6</span> &divide; 4<span class="sroot">3</span> = (8 &divide; 4)<span class="sroot">6 &divide; 3</span> = <strong>2<span class="sroot">2</span></strong>
- </li>
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