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161 lines
6.9 KiB
HTML
161 lines
6.9 KiB
HTML
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/surds.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:48:18 GMT -->
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<head>
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<title>Surds</title>
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<body id="bodybg">
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<div class="bg">
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<div id="stt"></div>
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<div id="hdr"></div>
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<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun" /></a></div>
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<div id="menuWide" class="menu">
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">Surds</h1>
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<p>When we can't simplify a number to remove a square root (or cube root etc) then it is a surd.</p>
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<div class="example">
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<p>Example: √<span style="text-decoration: overline;">2</span> (square root of 2) can't be simplified further so it is a <b>surd</b></p>
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</div>
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<div class="example">
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<p>Example: √<span style="text-decoration: overline;">4</span> (square root of 4) <b>can</b> be simplified (to 2), so it is <b>not a surd</b>!</p>
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</div>
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<p>Have a look at some more examples:</p>
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<div class="simple">
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<table border="0" align="center">
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<tr align="center">
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<th>Number</th>
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<th>Simplified</th>
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<th>As a Decimal</th>
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<th width="100">Surd or<br />
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not?</th>
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</tr>
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<tr align="center">
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<td height="9">√<span style="text-decoration: overline;">2</span></td>
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<td height="9">√<span style="text-decoration: overline;">2</span></td>
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<td height="9">1.4142135...(etc)</td>
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<td height="9"><b>Surd</b></td>
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</tr>
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<tr align="center">
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<td>√<span style="text-decoration: overline;">3</span></td>
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<td>√<span style="text-decoration: overline;">3</span></td>
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<td>1.7320508...(etc)</td>
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<td><b>Surd</b></td>
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</tr>
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<tr align="center">
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<td>√<span style="text-decoration: overline;">4</span></td>
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<td>2</td>
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<td>2</td>
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<td><i>Not a surd</i></td>
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</tr>
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<tr align="center">
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<td>√<span style="text-decoration: overline;">¼</span></td>
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<td>½</td>
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<td>0.5</td>
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<td><i>Not a surd</i></td>
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</tr>
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<tr align="center">
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<td><sup>3</sup>√<span style="text-decoration: overline;">11</span></td>
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<td><sup>3</sup>√<span style="text-decoration: overline;">11</span></td>
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<td>2.2239800...(etc)</td>
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<td><b>Surd</b></td>
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</tr>
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<tr align="center">
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<td><sup>3</sup>√<span style="text-decoration: overline;">27</span></td>
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<td>3</td>
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<td>3</td>
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<td><i>Not a surd</i></td>
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</tr>
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<tr align="center">
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<td><sup>5</sup>√<span style="text-decoration: overline;">3</span></td>
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<td><sup>5</sup>√<span style="text-decoration: overline;">3</span></td>
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<td>1.2457309...(etc)</td>
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<td><b>Surd</b></td>
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</tr>
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</table>
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<br />
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</div>
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<p>The surds have a decimal which goes on forever without repeating, and are <a href="irrational-numbers.html">Irrational Numbers</a>.</p>
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<table border="0" align="center">
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<tr>
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<td><img src="images/style/scroll.jpg" width="48" height="48" alt="scroll" /></td>
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<td>In fact "Surd" used to be another name for "Irrational", <br>
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but it is now used for a <b>root</b> that is irrational.</td>
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</tr>
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</table>
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<p> </p>
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<div class="words">
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<p>How did we get the word "Surd" ?</p>
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<p>Well around 820 AD <i>al-Khwarizmi</i> (the Persian guy who we get the name "Algorithm" from) called irrational numbers "'inaudible" ... this was later translated to the Latin <i><b>surdus</b></i> ("deaf" or "mute") </p>
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</div>
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<h2>Conclusion</h2>
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<div class="bigul">
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<ul>
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<li>When it is a <b>root</b> and <b>irrational</b>, it is a surd.</li>
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<li>But <b>not all</b> roots are surds. </li>
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</ul> </div>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(2043, 320, 2044, 3162, 3163, 3865, 3866, 3867, 3868, 3869);</script>
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</div>
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<div class="related">
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<a href="irrational-numbers.html">Irrational Numbers</a>
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<a href="square-root.html">Square Roots</a>
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<a href="numbers/simplify-square-roots.html">Simplifying Square Roots</a> <a href="scientific-calculator.html">Scientific Calculator</a> </div>
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<div id="copyrt">
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Copyright © 2017 MathsIsFun.com
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