{"id":2349,"date":"2021-11-26T15:36:49","date_gmt":"2021-11-26T20:36:49","guid":{"rendered":"https:\/\/www.alpharithms.com\/?p=2349"},"modified":"2022-06-16T15:23:48","modified_gmt":"2022-06-16T19:23:48","slug":"square-root-python","status":"publish","type":"post","link":"https:\/\/www.alpharithms.com\/square-root-python-493615\/","title":{"rendered":"Square Roots in Python: Be Mindful of Operator Precedence"},"content":{"rendered":"<p>Python offers developers a robust set of language features and built-in functions. Calculating the square root of a number is a task for which Python offers several options\u2014from operators to built-in library functions.\u00a0 Python&#8217;s simple syntax makes calculating the square root possible in a single line of code and, in many cases, with only three specified terms.<\/p>\n<p>There are some caveats, such as operator precedence, that might cause some issues. In this article, we&#8217;ll take a look at several approaches to calculating the square root in Python. We&#8217;ll also consider a few edge cases where syntactic oversights might lead to disastrous downstream effects.<\/p>\n<p><strong>TL;DR<\/strong> &#8211; Python offers developers several options. The following are the easiest to implement:<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Raise to a fractional power\r\n16**(1\/2)\r\n\r\n&gt;&gt;&gt; 4.0\r\n\r\n# Raise to a decimal power\r\n16**.5\r\n\r\n&gt;&gt;&gt; 4.0\r\n\r\n# Use Math's sqrt function\r\nfrom math import sqrt\r\nsqrt(16)\r\n\r\n&gt;&gt;&gt; 4.0<\/pre>\n<h2>Highlights<\/h2>\n<ul>\n<li>Python has an exponentiation operator that can be used to calculate root values.<\/li>\n<li>Square roots can be calculated in Python using the exponentiation operator and raising values to a power of <code class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">1\/2<\/code>.<\/li>\n<li>Forgetting about operator precedence can lead to disasters<\/li>\n<li>Python also offers a <code class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">sqrt()<\/code> function via the standard library&#8217;s math module.<\/li>\n<\/ul>\n<h2>Introduction<\/h2>\n<p>Python lets developers select from several convenient means of calculating the square root of a number. Since Python 3, developers can use the double-asterisk syntax (**) to indicate the exponentiation of a number to a fraction or decimal. This is referred to as the Python square operator and is used for calculating exponentiation.<\/p>\n<p>If we recall the laws governing fractional exponents, we can realize using the Python square operation with a fractional value can calculate root values. In this case, <strong>raising a number to the power of (1\/2) is equivalent to taking the square root<\/strong>.<\/p>\n<p>However, this is just one of several ways to calculate the square root using Python. The <code class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">math<\/code> module from Python&#8217;s standard library provides an optimized <code class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">sqrt()<\/code> function as well. In this article, we&#8217;ll take a look at each of these and discuss when one might be preferred over another. To get started, let&#8217;s take Python&#8217;s exponentiation operator for a test drive.<\/p>\n<h2>Python Exponentiation 101<\/h2>\n<p>Python interprets two successive asterisk symbols without spacing to signify the previous term being raised to the value directly proceeding the asterisks. In other words, 2<sup>8<\/sup> is coded as <code class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">2**8<\/code>.\u00a0 Let&#8217;s see what this looks like in code:<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># no spaces\r\n2**8\r\n&gt;&gt;&gt; 256\r\n\r\n# Trailing space\r\n2** 8\r\n&gt;&gt;&gt; 256\r\n\r\n# Leading space\r\n2 **8\r\n\r\n# Double space\r\n2 ** 8\r\n&gt;&gt;&gt; 256\r\n\r\n# Lotsa Space\r\n2                 **    8\r\n&gt;&gt;&gt; 256<\/pre>\n<p>Here we see Python following the convention of many other popular programming languages\u2014using the <strong>double-asterisk notation for exponentiation<\/strong>. However, Python&#8217;s interpretation of whitespace affords developers a unique ability to mix in as much whitespace as desired.<\/p>\n<h2>Fractional Exponentiation<\/h2>\n<p>For those familiar with exponent rules, you might recall that raising a base number to a fractional exponent is the same as taking the root value of the fraction&#8217;s denominator. For a deeper dive into fractional exponents, check out this <a href=\"https:\/\/www.kristakingmath.com\/blog\/fractional-exponents\">great discussion by Krista King<\/a>. For our purposes here, just keep in mind the following equation:<\/p>\n<figure id=\"attachment_2350\" aria-describedby=\"caption-attachment-2350\" style=\"width: 1024px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.alpharithms.com\/wp-content\/uploads\/2349\/square-root-exponentiation-formula-alpharithms.jpg\"><img fetchpriority=\"high\" decoding=\"async\" class=\"border-image wp-image-2350 size-full\" title=\"square-root-exponentiation-formula-alpharithms\" src=\"https:\/\/www.alpharithms.com\/wp-content\/uploads\/2349\/square-root-exponentiation-formula-alpharithms.jpg\" alt=\"square root exponentiation formula alpharithms\" width=\"1024\" height=\"576\" srcset=\"https:\/\/www.alpharithms.com\/wp-content\/uploads\/2349\/square-root-exponentiation-formula-alpharithms.jpg 1024w, https:\/\/www.alpharithms.com\/wp-content\/uploads\/2349\/square-root-exponentiation-formula-alpharithms-300x169.jpg 300w, https:\/\/www.alpharithms.com\/wp-content\/uploads\/2349\/square-root-exponentiation-formula-alpharithms-768x432.jpg 768w, https:\/\/www.alpharithms.com\/wp-content\/uploads\/2349\/square-root-exponentiation-formula-alpharithms-450x253.jpg 450w, https:\/\/www.alpharithms.com\/wp-content\/uploads\/2349\/square-root-exponentiation-formula-alpharithms-780x439.jpg 780w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption id=\"caption-attachment-2350\" class=\"wp-caption-text\">When raising a value to an exponent the numerator becomes the power of the base and the denominator is the root taken. (click to enlarge)<\/figcaption><\/figure>\n<p>For our discussion, we will assume that the numerator will always be 1 (a in the image above) and the denominator will always be 2( b in the image above.) In other words\u2014square roots are always calculated by raising a value to the <code class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">1\/2<\/code> power. Let&#8217;s see how this works.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Get the square root of 4 via fractional exponentiation\r\n4 ** 1\/2\r\n\r\n&gt;&gt;&gt; 2.0\r\n\r\n# Get the square root of 16 via fractional exponentiation\r\n16 ** 1\/2\r\n\r\n&gt;&gt;&gt; 8.0   \r\n\r\n# Make sure to use parenthesis when using fractional exponents\r\n16 ** (1\/2)\r\n\r\n&gt;&gt;&gt; 4.0<\/pre>\n<p>Here we see one\u00a0<em>very<\/em> important caveat of using fractional exponents to get the square root in Python\u2014one must use parenthesis! Python&#8217;s <a href=\"https:\/\/docs.python.org\/3\/reference\/expressions.html#operator-precedence\">operator precedence<\/a> dictates that exponentiation comes before division.<\/p>\n<p>In the example of <code class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">16 ** 1\/2<\/code> above, that means 16 is raised to the power of 1 and that result is divided by 2 (<code class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">16 ** 1 = 16 \/ 2 = 8.<\/code>) Adding the parenthesis ensures the fractional value is evaluated prior to exponentiation as such: (<code class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">16 ** (1 \/ 2) = 16 ** .5 = 4.0<\/code>.)<\/p>\n<h2>Decimal Exponentiation<\/h2>\n<p>In considering the caveat of having our fractional powers in parenthesis, we can realize using a decimal value will avoid potential confusion. That is, use the resulting value of our fraction initially rather than having that value calculated during runtime. For example, let&#8217;s see what happens when we substitute in <code class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">1\/2<\/code>&#8216;s decimal value.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Get decimal value of fraction\r\n1 \/ 2\r\n\r\n&gt;&gt;&gt; 0.5\r\n\r\n# Use decimal value as exponent\r\n16 ** 0.5\r\n\r\n&gt;&gt;&gt; 4\r\n\r\n# Drop the leading zero\r\n16 ** .5\r\n\r\n&gt;&gt;&gt; 4<\/pre>\n<p>Here we see that no parentheses are required when pre-calculating the decimal value. Conceptually, this is no different than adding parentheses\u2014both approaches ensure the 1\/2 operation happens before the exponentiation. It&#8217;s also worth noting that we needn&#8217;t both with leading zeroes.<\/p>\n<h2>The Math Module<\/h2>\n<p>The Python standard library comes with plenty of tools to help developers tackle common programming tasks. Calculating square roots is no exception and Python offers the <a href=\"https:\/\/docs.python.org\/3\/library\/math.html\">Math module complete with a square root function<\/a> to lend a hand in calculating square root values. The code below showcases the simplicity by which this function offers utility:<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">from math import sqrt\r\n\r\n# Calculate square root of 16\r\nsqrt(16)\r\n\r\n&gt;&gt;&gt; 4.0<\/pre>\n<h2>Final Thoughts<\/h2>\n<p>Python is an incredible language that simplifies the syntax for so many common development tasks it&#8217;s hard to keep count. As we&#8217;ve seen here, calculating the square root in Python is no exception\u2014with developers having several options at their disposal. Personally, I&#8217;m a fan of using the exponentiation operator for the simple fact it avoids importing the math module. If this approach seems attractive just don&#8217;t forget to add the parentheses!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Python offers developers a robust set of language features and built-in functions. Calculating the square root of a number is a task for which Python offers several options\u2014from operators to built-in library functions.\u00a0 Python&#8217;s simple syntax makes calculating the square root possible in a single line of code and, in many cases, with only three [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":2358,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[655,10],"tags":[599,598,364,143,597],"acf":[],"_links":{"self":[{"href":"https:\/\/www.alpharithms.com\/wp-json\/wp\/v2\/posts\/2349"}],"collection":[{"href":"https:\/\/www.alpharithms.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.alpharithms.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.alpharithms.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.alpharithms.com\/wp-json\/wp\/v2\/comments?post=2349"}],"version-history":[{"count":4,"href":"https:\/\/www.alpharithms.com\/wp-json\/wp\/v2\/posts\/2349\/revisions"}],"predecessor-version":[{"id":2357,"href":"https:\/\/www.alpharithms.com\/wp-json\/wp\/v2\/posts\/2349\/revisions\/2357"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.alpharithms.com\/wp-json\/wp\/v2\/media\/2358"}],"wp:attachment":[{"href":"https:\/\/www.alpharithms.com\/wp-json\/wp\/v2\/media?parent=2349"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.alpharithms.com\/wp-json\/wp\/v2\/categories?post=2349"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.alpharithms.com\/wp-json\/wp\/v2\/tags?post=2349"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}