diff options
Diffstat (limited to 'lessons/matematika/pangkat-akar')
| -rw-r--r-- | lessons/matematika/pangkat-akar/akar.html | 42 | ||||
| -rw-r--r-- | lessons/matematika/pangkat-akar/latihan.html | 58 | ||||
| -rw-r--r-- | lessons/matematika/pangkat-akar/pangkat.html | 8 |
3 files changed, 54 insertions, 54 deletions
diff --git a/lessons/matematika/pangkat-akar/akar.html b/lessons/matematika/pangkat-akar/akar.html index 35ed018..4665ae0 100644 --- a/lessons/matematika/pangkat-akar/akar.html +++ b/lessons/matematika/pangkat-akar/akar.html @@ -61,57 +61,57 @@ <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="root">16</span> = 4</b></li> - <li>5<sup>2</sup> = 25, <b>so <span class="root">25</span> = 5</b></li> - <li>10<sup>2</sup> = 100, <b>so <span class="root">100</span> = 10</b></li> + <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="root">60</span></strong><br> - <span class="root">60</span> = <span class="root">4 × 15</span> = 2<span class="root">15</span><br> + <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="root">48</span></strong><br> - <span class="root">48</span> = <span class="root">16 × 3</span> = 4<span class="root">3</span><br> + <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="root">125</span></strong><br> - <span class="root">125</span> = <span class="root">25 × 5</span> = 5<span class="root">5</span><br> + <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="root">c</span> + b<span class="root">c</span> = (a + b)<span class="root">c</span></strong> + <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="root">2</span> + 4<span class="root">2</span> = (3 + 4)<span class="root">2</span> = <strong>7<span class="root">2</span></strong></li> - <li><span class="root">5</span> + 3<span class="root">5</span> = (1 + 3)<span class="root">5</span> = <strong>4<span class="root">5</span></strong></li> + <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="root">c</span> - b<span class="root">c</span> = (a - b)<span class="root">c</span></strong> + <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="root">3</span> - 4<span class="root">3</span> = (7 - 4)<span class="root">3</span> = <strong>3<span class="root">2</span></strong></li> - <li>10<span class="root">6</span> - 5<span class="root">6</span> = (10 - 5)<span class="root">6</span> = <strong>5<span class="root">6</span></strong></li> + <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="root">c</span> × b<span class="root">d</span> = (a × b)<span class="root">c × d</span></strong> + <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="root">2</span> × <span class="root">5</span> = <strong><span class="root">10</span></strong></li> - <li>3<span class="root">2</span> × 4<span class="root">3</span> = (3 × 4)<span class="root">2 × 3</span> = <strong>12<span class="root">6</span></strong></li> - <li>2<span class="root">5</span> × 3<span class="root">5</span> = (2 × 3)(5) = 6(5) = <strong>30</strong></li> + <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="root">c</span> ÷ b<span class="root">d</span> = (a ÷ b)<span class="root">c ÷ d</span></strong> + <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="root">6</span> ÷ 4<span class="root">3</span> = (8 ÷ 4)<span class="root">6 ÷ 3</span> = <strong>2<span class="root">2</span></strong> + 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> </section> diff --git a/lessons/matematika/pangkat-akar/latihan.html b/lessons/matematika/pangkat-akar/latihan.html index a019254..701a456 100644 --- a/lessons/matematika/pangkat-akar/latihan.html +++ b/lessons/matematika/pangkat-akar/latihan.html @@ -63,13 +63,13 @@ <h2 id="questions--pangkat">Pangkat</h1> <li style="margin-top: 10px;">8p<sup>2</sup>q × 2pq<sup>3</sup></li> <li style="margin-top: 10px;">64<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>2</sub></span></sup> + 81<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>3</sub></span></sup></li> - <li style="margin-top: 10px;">2<span class="root">5</span> + 3<span class="root">20</span> - 4<span class="root">5</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></li> <h2 id="questions--rasional">Merasionalkan Akar</h2> - <li style="margin-top: 10px;"><span class="frac"><sup>4</sup><span>⁄</span><sub><span class="root">5</span></sub></span></li> - <li style="margin-top: 10px;"><span class="frac"><sup>3<span class="root">5</span></sup><span>⁄</span><sub>2<span class="root">3</span></sup></sub></span></li> - <li style="margin-top: 10px;"><span class="frac"><sup>5</sup><span>⁄</span><sub><span class="root">3</span> - <span class="root">2</span></sub></span></li> - <li style="margin-top: 10px;"><span class="frac"><sup><span class="root">5</span> - <span class="root">7</span></sup><span>⁄</span><sub><span class="root">5</span> - <span class="root">2</span></sub></span></li> + <li style="margin-top: 10px;"><span class="frac"><sup>4</sup><span>⁄</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>⁄</span><sub>2<span class="sroot">3</span></sup></sub></span></li> + <li style="margin-top: 10px;"><span class="frac"><sup>5</sup><span>⁄</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>⁄</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> ÷ 2pq</li> @@ -84,40 +84,40 @@ <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>⁄</span><sub>2</sub></span></sup> + 81<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>3</sub></span></sup><br> - = <span class="root">64</span> + <sup>3</sup><span class="root">81</span><br> - = 8 + <sup>3</sup><span class="root">81</span> + = <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="root">5</span> + 3<span class="root">20</span> - 4<span class="root">5</span><br> - = 6<span class="root">5</span> + 3<span class="root">20</span><br> - = 6<span class="root">5</span> + 3<span class="root">4 × 5</span><br> - = 6<span class="root">5</span> + 3<span class="root">2<sup>2</sup> × 5</span><br> - = 6<span class="root">5</span> + 3 × 2<span class="root">5</span><br> - = 6<span class="root">5</span> + 6<span class="root">5</span><br> - = <strong>12<span class="root">5</span></strong><br> + 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 × 5</span><br> + = 6<span class="sroot">5</span> + 3<span class="sroot">2<sup>2</sup> × 5</span><br> + = 6<span class="sroot">5</span> + 3 × 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>⁄</span><sub><span class="root">5</span></sub></span><br> - = <span class="frac"><sup>4</sup><span>⁄</span><sub><span class="root">5</span></sub></span> × <span class="frac"><sup><span class="root">5</span></sup><span>⁄</span><sub><span class="root">5</span></sub></span> = <strong><span class="frac"><sup>4<span class="root">5</span></sup><span>⁄</span><sub>5</sub></span></strong> + <span class="frac"><sup>4</sup><span>⁄</span><sub><span class="sroot">5</span></sub></span><br> + = <span class="frac"><sup>4</sup><span>⁄</span><sub><span class="sroot">5</span></sub></span> × <span class="frac"><sup><span class="sroot">5</span></sup><span>⁄</span><sub><span class="sroot">5</span></sub></span> = <strong><span class="frac"><sup>4<span class="sroot">5</span></sup><span>⁄</span><sub>5</sub></span></strong> </li> <li style="margin-top: 10px;"> - <span class="frac"><sup>3<span class="root">5</span></sup><span>⁄</span><sub>2<span class="root">3</span></sup></sub></span><br> - = <span class="frac"><sup>3<span class="root">5</span></sup><span>⁄</span><sub>2<span class="root">3</span></sup></sub></span> × <span class="frac"><sup><span class="root">3</span></sup><span>⁄</span><sub><span class="root">3</span></sup></sub></span><br> - = <span class="frac"><sup><span style="text-decoration: line-through;">3</span><span class="root">15</span></sup><span>⁄</span><sub>2 × <span style="text-decoration: line-through;">3</span></sup></sub></span><br> - = <strong><span class="frac"><sup><span class="root">15</span></sup><span>⁄</span><sub>2</sup></sub></span></strong> + <span class="frac"><sup>3<span class="sroot">5</span></sup><span>⁄</span><sub>2<span class="sroot">3</span></sup></sub></span><br> + = <span class="frac"><sup>3<span class="sroot">5</span></sup><span>⁄</span><sub>2<span class="sroot">3</span></sup></sub></span> × <span class="frac"><sup><span class="sroot">3</span></sup><span>⁄</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>⁄</span><sub>2 × <span style="text-decoration: line-through;">3</span></sup></sub></span><br> + = <strong><span class="frac"><sup><span class="sroot">15</span></sup><span>⁄</span><sub>2</sup></sub></span></strong> </li> <li style="margin-top: 10px;"> - <span class="frac"><sup>5</sup><span>⁄</span><sub><span class="root">3</span> - <span class="root">2</span></sub></span><br> - = <span class="frac"><sup>5</sup><span>⁄</span><sub><span class="root">3</span> - <span class="root">2</span></sub></span> × <span class="frac"><sup><span class="root">3</span> + <span class="root">2</span></sup><span>⁄</span><sub><span class="root">3</span> + <span class="root">2</span></sub></span><br> - = <span class="frac"><sup>5(<span class="root">3</span> + <span class="root">2</span>)</sup><span>⁄</span><sub>(<span class="root">3</span>)<sup>2</sup> - (<span class="root">2</span>)<sup>2</sup></sub></span><br> - = <span class="frac"><sup>5(<span class="root">3</span> + <span class="root">2</span>)</sup><span>⁄</span><sub>3 - 2</sub></span> = <span class="frac"><sup>5(<span class="root">3</span> + <span class="root">2</span>)</sup><span>⁄</span><sub>1</sub></span><br> - = <strong>5(<span class="root">3</span> + <span class="root">2</span>)</strong> + <span class="frac"><sup>5</sup><span>⁄</span><sub><span class="sroot">3</span> - <span class="sroot">2</span></sub></span><br> + = <span class="frac"><sup>5</sup><span>⁄</span><sub><span class="sroot">3</span> - <span class="sroot">2</span></sub></span> × <span class="frac"><sup><span class="sroot">3</span> + <span class="sroot">2</span></sup><span>⁄</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>⁄</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>⁄</span><sub>3 - 2</sub></span> = <span class="frac"><sup>5(<span class="sroot">3</span> + <span class="sroot">2</span>)</sup><span>⁄</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="root">5</span> - <span class="root">7</span></sup><span>⁄</span><sub><span class="root">5</span> - <span class="root">2</span></sub></span><br> - = <span class="frac"><sup><span class="root">5</span> - <span class="root">7</span></sup><span>⁄</span><sub><span class="root">5</span> - <span class="root">2</span></sub></span> × <span class="frac"><sup><span class="root">5</span> + <span class="root">2</span></sup><span>⁄</span><sub><span class="root">5</span> + <span class="root">2</span></sub></span><br> - = <span class="frac"><sup>(<span class="root">5</span> - <span class="root">7</span>) × (<span class="root">5</span> + <span class="root">2</span>)</sup><span>⁄</span><sub>(<span class="root">5</span>)<sup>2</sup> - (<span class="root">2</span>)<sup>2</sup></sub></span><br> - = <span class="frac"><sup>5 + <span class="root">10</span> - <span class="root">35</span> - <span class="root">14</span></sup><span>⁄</span><sub>5 - 2</sub></span> = <strong><span class="frac"><sup>5 + <span class="root">10</span> - <span class="root">35</span> - <span class="root">14</span></sup><span>⁄</span><sub>3</sub></span></strong> + <span class="frac"><sup><span class="sroot">5</span> - <span class="sroot">7</span></sup><span>⁄</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>⁄</span><sub><span class="sroot">5</span> - <span class="sroot">2</span></sub></span> × <span class="frac"><sup><span class="sroot">5</span> + <span class="sroot">2</span></sup><span>⁄</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>) × (<span class="sroot">5</span> + <span class="sroot">2</span>)</sup><span>⁄</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>⁄</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>⁄</span><sub>3</sub></span></strong> </li> <li style="margin-top: 10px;"> (8p<sup>2</sup>3)<sup>3</sup> ÷ 2pq <br> diff --git a/lessons/matematika/pangkat-akar/pangkat.html b/lessons/matematika/pangkat-akar/pangkat.html index 4061c82..7c7ccce 100644 --- a/lessons/matematika/pangkat-akar/pangkat.html +++ b/lessons/matematika/pangkat-akar/pangkat.html @@ -103,15 +103,15 @@ <h1 id="fractional-exponent">Fractional Exponent</h1> <img src="/assets/images/math/fractional_exponent.svg" alt=""> <p>x <sup><span class="frac"><sup>y</sup><span>⁄</span><sub>z</sub></span></sup> = - <sup>z</sup><span><span class="root">x</span><sup style="font-size: small;">y</sup><span></span></span></p> + <sup>z</sup><span><span class="sroot">x</span><sup style="font-size: small;">y</sup><span></span></span></p> <h2 id="fractional-exponent--examples">Examples</h2> <ul> <li>5 <sup><span class="frac"><sup>1</sup><span>⁄</span><sub>2</sub></span></sup> = - <sup>2</sup><span><span class="root">5</span></span></li> + <sup>2</sup><span><span class="sroot">5</span></span></li> <li>7 <sup><span class="frac"><sup>2</sup><span>⁄</span><sub>3</sub></span></sup> = - <sup>3</sup><span><span class="root">7<sup>2</sup></span></span></li> + <sup>3</sup><span><span class="sroot">7<sup>2</sup></span></span></li> </ul> - <p><strong>Small Note:</strong> 2</sup><span class="root">x</span> or <span class="root">x</span> menans square root. The 2 before root should be removed. The 2 is only present for easier purposes.<br>3</sup><span><span class="root">x</span> means cubic root.</p> + <p><strong>Small Note:</strong> 2</sup><span class="sroot">x</span> or <span class="sroot">x</span> menans square root. The 2 before root should be removed. The 2 is only present for easier purposes.<br>3</sup><span><span class="sroot">x</span> means cubic root.</p> <h1 id="exponential-equation">Exponential Equation</h1> <ol> |