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authoraltaf-creator <athaalaa@gmail.com>2023-09-25 20:18:57 +0700
committeraltaf-creator <athaalaa@gmail.com>2023-09-25 20:18:57 +0700
commit18670260285d25b14921a89fae60089da334c921 (patch)
treedbd0d0a17a7704e963504744e21a273b9c374b3b /lessons-locked/matematika/pangkat-akar/latihan.html
parent7420ea9926c6cca698efa670d837a1cd753c4931 (diff)
Unlocked website, added rationalising roots
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-<!DOCTYPE html>
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- <meta http-equiv="X-UA-Compatible" content="IE=edge">
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- <title>Al Azhar 9th Grade Lesson Notes</title>
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- <img src="/assets/images/master.svg" alt="" class="sidebar-logo">
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- <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">Exercise</h1>
- <h3 class="banner-text" id="banner-txt">Chapter 1</h3>
- </div>
- </div>
-
- <div class="chip-container" id="chip-container">
- <div class="chip"><span>❓ Unchecked</span></div>
- </div>
-
- <div id="main">
- <section>
- <h1 id="questions">Pertanyaan</h1>
- <ol>
- <h2 id="questions--pangkat">Pangkat</h1>
- <li style="margin-top: 10px;">8p<sup>2</sup>q &times; 2pq<sup>3</sup></li>
- <li style="margin-top: 10px;">64<sup><span class="frac"><sup>1</sup><span>&frasl;</span><sub>2</sub></span></sup> + 81<sup><span class="frac"><sup>1</sup><span>&frasl;</span><sub>3</sub></span></sup></li>
- <li style="margin-top: 10px;">2<span class="sroot">5</span> + 3<span class="sroot">20</span> - 4<span class="sroot">5</span></li>
-
- <h2 id="questions--rasional">Merasionalkan Akar</h2>
- <li style="margin-top: 10px;"><span class="frac"><sup>4</sup><span>&frasl;</span><sub><span class="sroot">5</span></sub></span></li>
- <li style="margin-top: 10px;"><span class="frac"><sup>3<span class="sroot">5</span></sup><span>&frasl;</span><sub>2<span class="sroot">3</span></sup></sub></span></li>
- <li style="margin-top: 10px;"><span class="frac"><sup>5</sup><span>&frasl;</span><sub><span class="sroot">3</span> - <span class="sroot">2</span></sub></span></li>
- <li style="margin-top: 10px;"><span class="frac"><sup><span class="sroot">5</span> - <span class="sroot">7</span></sup><span>&frasl;</span><sub><span class="sroot">5</span> - <span class="sroot">2</span></sub></span></li>
-
- <h2 id="question--operasi-pangkat">Operasi Pangkat</h2>
- <li style="margin-top: 10px;">(8p<sup>2</sup>3)<sup>3</sup> &divide; 2pq</li>
- <li style="margin-top: 10px;"><span class="frac"><sup>(a<sup><span class="frac"><sup>1</sup><span>&frasl;</span><sub>3</sub></span></sup>b<sup><span class="frac"><sup>1</sup><span>&frasl;</span><sub>3</sub></span></sup>)<sup>6</sup></sup><span>&frasl;</span><sub>(a<sup><span class="frac"><sup>2</sup><span>&frasl;</span><sub>3</sub></span></sup>b<sup><span class="frac"><sup>4</sup><span>&frasl;</span><sub>3</sub></span></sup>)<sup>9</sup></sup></sub></span></li>
-
- <h2 id="question--persamaan-pangkat">Persamaan Pangkat</h2>
- <li style="margin-top: 10px;">2<sup>x + 8</sup> = 64</li>
- <li style="margin-top: 10px;">16<sup>2x + 3</sup> = 32</li>
- </ol>
- <h1 id="jawaban">Jawaban</h1>
- <ol>
- <li style="margin-top: 10px;">16p<sup>3</sup>q<sup>4</sup></li>
- <li style="margin-top: 10px;">
- 64<sup><span class="frac"><sup>1</sup><span>&frasl;</span><sub>2</sub></span></sup> + 81<sup><span class="frac"><sup>1</sup><span>&frasl;</span><sub>3</sub></span></sup><br>
- = <span class="sroot">64</span> + <sup>3</sup><span class="sroot">81</span><br>
- = 8 + <sup>3</sup><span class="sroot">81</span>
- </li>
- <li style="margin-top: 10px;">
- 2<span class="sroot">5</span> + 3<span class="sroot">20</span> - 4<span class="sroot">5</span><br>
- = 6<span class="sroot">5</span> + 3<span class="sroot">20</span><br>
- = 6<span class="sroot">5</span> + 3<span class="sroot">4 &times; 5</span><br>
- = 6<span class="sroot">5</span> + 3<span class="sroot">2<sup>2</sup> &times; 5</span><br>
- = 6<span class="sroot">5</span> + 3 &times; 2<span class="sroot">5</span><br>
- = 6<span class="sroot">5</span> + 6<span class="sroot">5</span><br>
- = <strong>12<span class="sroot">5</span></strong><br>
- </li>
- <li style="margin-top: 10px;">
- <span class="frac"><sup>4</sup><span>&frasl;</span><sub><span class="sroot">5</span></sub></span><br>
- = <span class="frac"><sup>4</sup><span>&frasl;</span><sub><span class="sroot">5</span></sub></span> &times; <span class="frac"><sup><span class="sroot">5</span></sup><span>&frasl;</span><sub><span class="sroot">5</span></sub></span> = <strong><span class="frac"><sup>4<span class="sroot">5</span></sup><span>&frasl;</span><sub>5</sub></span></strong>
- </li>
- <li style="margin-top: 10px;">
- <span class="frac"><sup>3<span class="sroot">5</span></sup><span>&frasl;</span><sub>2<span class="sroot">3</span></sup></sub></span><br>
- = <span class="frac"><sup>3<span class="sroot">5</span></sup><span>&frasl;</span><sub>2<span class="sroot">3</span></sup></sub></span> &times; <span class="frac"><sup><span class="sroot">3</span></sup><span>&frasl;</span><sub><span class="sroot">3</span></sup></sub></span><br>
- = <span class="frac"><sup><span style="text-decoration: line-through;">3</span><span class="sroot">15</span></sup><span>&frasl;</span><sub>2 &times; <span style="text-decoration: line-through;">3</span></sup></sub></span><br>
- = <strong><span class="frac"><sup><span class="sroot">15</span></sup><span>&frasl;</span><sub>2</sup></sub></span></strong>
- </li>
- <li style="margin-top: 10px;">
- <span class="frac"><sup>5</sup><span>&frasl;</span><sub><span class="sroot">3</span> - <span class="sroot">2</span></sub></span><br>
- = <span class="frac"><sup>5</sup><span>&frasl;</span><sub><span class="sroot">3</span> - <span class="sroot">2</span></sub></span> &times; <span class="frac"><sup><span class="sroot">3</span> + <span class="sroot">2</span></sup><span>&frasl;</span><sub><span class="sroot">3</span> + <span class="sroot">2</span></sub></span><br>
- = <span class="frac"><sup>5(<span class="sroot">3</span> + <span class="sroot">2</span>)</sup><span>&frasl;</span><sub>(<span class="sroot">3</span>)<sup>2</sup> - (<span class="sroot">2</span>)<sup>2</sup></sub></span><br>
- = <span class="frac"><sup>5(<span class="sroot">3</span> + <span class="sroot">2</span>)</sup><span>&frasl;</span><sub>3 - 2</sub></span> = <span class="frac"><sup>5(<span class="sroot">3</span> + <span class="sroot">2</span>)</sup><span>&frasl;</span><sub>1</sub></span><br>
- = <strong>5(<span class="sroot">3</span> + <span class="sroot">2</span>)</strong>
- </li>
- <li style="margin-top: 10px;">
- <span class="frac"><sup><span class="sroot">5</span> - <span class="sroot">7</span></sup><span>&frasl;</span><sub><span class="sroot">5</span> - <span class="sroot">2</span></sub></span><br>
- = <span class="frac"><sup><span class="sroot">5</span> - <span class="sroot">7</span></sup><span>&frasl;</span><sub><span class="sroot">5</span> - <span class="sroot">2</span></sub></span> &times; <span class="frac"><sup><span class="sroot">5</span> + <span class="sroot">2</span></sup><span>&frasl;</span><sub><span class="sroot">5</span> + <span class="sroot">2</span></sub></span><br>
- = <span class="frac"><sup>(<span class="sroot">5</span> - <span class="sroot">7</span>) &times; (<span class="sroot">5</span> + <span class="sroot">2</span>)</sup><span>&frasl;</span><sub>(<span class="sroot">5</span>)<sup>2</sup> - (<span class="sroot">2</span>)<sup>2</sup></sub></span><br>
- = <span class="frac"><sup>5 + <span class="sroot">10</span> - <span class="sroot">35</span> - <span class="sroot">14</span></sup><span>&frasl;</span><sub>5 - 2</sub></span> = <strong><span class="frac"><sup>5 + <span class="sroot">10</span> - <span class="sroot">35</span> - <span class="sroot">14</span></sup><span>&frasl;</span><sub>3</sub></span></strong>
- </li>
- <li style="margin-top: 10px;">
- (8p<sup>2</sup>3)<sup>3</sup> &divide; 2pq <br>
- = (24p<sup>2</sup>)<sup>3</sup> &divide; 2pq <br>
- = 24<sup>3</sup> p<sup>6</sup> &divide; 2pq <br>
- = <strong>6912p<sup>5</sup> &divide; q</strong>
- </li>
- <li style="margin-top: 10px;">
- = <span class="frac"><sup>(a<sup><span class="frac"><sup>1</sup><span>&frasl;</span><sub>3</sub></span></sup>b<sup><span class="frac"><sup>1</sup><span>&frasl;</span><sub>3</sub></span></sup>)<sup>6</sup></sup><span>&frasl;</span><sub>(a<sup><span class="frac"><sup>2</sup><span>&frasl;</span><sub>3</sub></span></sup>b<sup><span class="frac"><sup>4</sup><span>&frasl;</span><sub>3</sub></span></sup>)<sup>9</sup></sup></sub></span><br>
- = <span class="frac">
- <sup>(a<sup><span class="frac"><sup>1</sup><span>&frasl;</span><sub>3</sub></span></sup>)<sup>6</sup> (b<sup><span class="frac"><sup>1</sup><span>&frasl;</span><sub>3</sub></span></sup>)<sup>6</sup></sup>
- <span>&frasl;</span>
- <sub>(a<sup><span class="frac"><sup>2</sup><span>&frasl;</span><sub>3</sub></span></sup>)<sup>9</sup> (b<sup><span class="frac"><sup>4</sup><span>&frasl;</span><sub>3</sub></span></sup>)<sup>9</sup></sub>
- </span><br>
- = <span class="frac">
- <sup>a<sup>2</sup> b<sup>2</sup></sup>
- <span>&frasl;</span>
- <sub>a<sup>6</sup> b<sup>12</sup></sub>
- </span><br>
- = <strong>a<sup>-4</sup> b<sup>-10</sup></strong>
- </li>
- <li style="margin-top: 10px;">
- 2<sup>x + 8</sup> = 64 <br>
- = <span style="text-decoration: line-through;">2</span><sup>x + 8</sup> = <span style="text-decoration: line-through;">2</span><sup>6</sup><br>
- = x + 8 = 6 <br>
- = x = 6 - 8 <br>
- = <strong>x = -2</strong>
- </li>
- <li style="margin-top: 10px;">
- 16<sup>2x + 3</sup> = 32 <br>
- = (2<sup>4</sup>)<sup>2x + 3</sup> = 2<sup>6</sup><br>
- = <span style="text-decoration: line-through;">2</span><sup>8x + 12</sup> = <span style="text-decoration: line-through;">2</span><sup>6</sup> <br>
- = 8x + 12 = 6 <br>
- = 8x = 6 - 12 <br>
- = 8x = 6 <br>
- = x = <span class="frac"><sup>-6</sup><span>&frasl;</span><sub>8</sub></span><br>
- = <strong>x = -<span class="frac"><sup>3</sup><span>&frasl;</span><sub>4</sub></span></strong>
- </li>
- </ol>
- </section>
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