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| author | altaf-creator <athaalaa@gmail.com> | 2023-09-25 20:18:57 +0700 |
|---|---|---|
| committer | altaf-creator <athaalaa@gmail.com> | 2023-09-25 20:18:57 +0700 |
| commit | 18670260285d25b14921a89fae60089da334c921 (patch) | |
| tree | dbd0d0a17a7704e963504744e21a273b9c374b3b /lessons/matematika/pangkat-akar/akar.html | |
| parent | 7420ea9926c6cca698efa670d837a1cd753c4931 (diff) | |
Unlocked website, added rationalising roots
Diffstat (limited to 'lessons/matematika/pangkat-akar/akar.html')
| -rw-r--r-- | lessons/matematika/pangkat-akar/akar.html | 170 |
1 files changed, 170 insertions, 0 deletions
diff --git a/lessons/matematika/pangkat-akar/akar.html b/lessons/matematika/pangkat-akar/akar.html new file mode 100644 index 0000000..1bacf4c --- /dev/null +++ b/lessons/matematika/pangkat-akar/akar.html @@ -0,0 +1,170 @@ +<!DOCTYPE html> +<html lang="en"> + +<head> + <meta charset="UTF-8"> + <meta http-equiv="X-UA-Compatible" content="IE=edge"> + <meta name="viewport" content="width=device-width, initial-scale=1.0"> + <link rel="stylesheet" href="/style.css"> + <link rel="icon" href="/assets/images/master.svg"> + <title>Al Azhar 9th Grade Lesson Notes</title> + <link rel="apple-touch-icon" sizes="180x180" href="/apple-touch-icon.png"> + <link rel="icon" type="image/png" sizes="32x32" href="/favicon-32x32.png"> + <link rel="icon" type="image/png" sizes="16x16" href="/favicon-16x16.png"> + <link rel="manifest" href="/site.webmanifest"> + <script src="https://kit.fontawesome.com/d279a1f519.js" crossorigin="anonymous"></script> + <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.css" + integrity="sha384-pRsDYiLLocCzWnUN/YEr9TBTTaZOUi5x8adKfqi6Qt44lDaFkoP++x1j2ohSMtdf" crossorigin="anonymous"> + <script src="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.js" + integrity="sha384-tMzugJpfLv7v0f+KXzNMqNCC6sVzLMM3sCnZDgzy0lcO/0h3sAkEBg/URFcV0JpE" + crossorigin="anonymous"></script> +</head> + +<body> + <div class="fixed-top-btn-container" id="topbtn"> + <a class="fixed-top-btn menu-btn" onclick="toggleNav()" href="javascript:void(0)"><i class="fa-solid fa-bars"></i></a> + <a href="../" class="fixed-top-btn back-btn"><i class="fa-solid fa-chevron-left"></i></a> + </div> + <div id="console"></div> + <div id="sidebar"> + <div> + <a href="/index.html"> + <img src="/assets/images/master.svg" alt="" class="sidebar-logo"> + </a> + + <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> + </div> + + <div> + <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> + + + <hr class="divider"> + <div id="toc"> + <h4>Table of Contents</h4> + </div> + </div> + </div> + + <div class="banner-container" id="banner"> + <div class="banner-bg" id="img-supplies"></div> + <div class="gradient-bg"></div> + <div class="banner-text-container"> + <h1 class="banner-text" id="banner-txt">Root</h1> + <h3 class="banner-text" id="banner-txt">Chapter 1</h3> + </div> + </div> + + <div class="chip-container" id="chip-container"> + <div class="chip"><span>✅ Verified</span></div> + </div> + + <div id="main"> + <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 × 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 × 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 × 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> × b<span class="sroot">d</span> = (a × b)<span class="sroot">c × d</span></strong> + <ul> + <li><span class="sroot">2</span> × <span class="sroot">5</span> = <strong><span class="sroot">10</span></strong></li> + <li>3<span class="sroot">2</span> × 4<span class="sroot">3</span> = (3 × 4)<span class="sroot">2 × 3</span> = <strong>12<span class="sroot">6</span></strong></li> + <li>2<span class="sroot">5</span> × 3<span class="sroot">5</span> = (2 × 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> ÷ b<span class="sroot">d</span> = (a ÷ b)<span class="sroot">c ÷ d</span></strong> + <ul> + <li> + 8<span class="sroot">6</span> ÷ 4<span class="sroot">3</span> = (8 ÷ 4)<span class="sroot">6 ÷ 3</span> = <strong>2<span class="sroot">2</span></strong> + </li> + </ul> + + <h2 id="rationalising">Rationalising Roots</h2> + <p>We can rationalise or simplify a fraction with a root denominator. To rationalise a root, multiply the fraction with a fraction of opposite roots. For example:</p> + <p><b>Example 1:</b></p> + <span id="id1"></span> + <script defer> + var element = document.getElementById("id1"); + katex.render(String.raw`\dfrac{3}{\sqrt{5}}\\ + = \dfrac{3}{\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}\\ + = \dfrac{3\sqrt{5}}{5} + `, element, { + throwOnError: false + }); + </script> + <p><b>Example 2:</b></p> + <span id="id2"></span> + <script defer> + var element = document.getElementById("id2"); + katex.render(String.raw`\dfrac{2}{3\sqrt{6}}\\ + = \dfrac{2}{3\sqrt{6}} \times \dfrac{\sqrt{6}}{\sqrt{6}}\\ + = \dfrac{2\sqrt{6}}{3 \cdot 6}\\ + = \dfrac{2\sqrt{6}}{18}\\ + = \dfrac{1}{9}\sqrt{6} + `, element, { + throwOnError: false + }); + </script> + <p><b>Example 3:</b></p> + <span id="id3"></span> + <script defer> + var element = document.getElementById("id3"); + katex.render(String.raw`\dfrac{8}{3 + \sqrt{7}}\\ + = \dfrac{8}{3 + \sqrt{7}} \times \dfrac{3 - \sqrt{7}}{3 - \sqrt{7}}\\ + = \dfrac{8(3 \cdot \sqrt{7})}{(3 \cdot \sqrt{7})(3 \cdot \sqrt{7})}\\ + = \dfrac{8(3 \cdot \sqrt{7})}{9 - 3\sqrt{7} + 3\sqrt{7} - 7}\\ + = \dfrac{8(3 \cdot \sqrt{7})}{9 - 7}\\ + = \dfrac{8(3 \cdot \sqrt{7})}{2} + `, element, { + throwOnError: false + }); + </script> + </section> + </div> + + <script src="/scripts/toc.js"></script> + <script src="/scripts/sidebar.js"></script> +</body> + +</html> |