{"id":116180,"date":"2022-03-02T12:05:23","date_gmt":"2022-03-02T18:05:23","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=116180"},"modified":"2026-03-28T11:49:50","modified_gmt":"2026-03-28T16:49:50","slug":"adding-and-subtracting-radical-expressions","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/adding-and-subtracting-radical-expressions\/","title":{"rendered":"Adding and Subtracting Radical Expressions"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_yEDU1JqWO70\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_yEDU1JqWO70\" data-source-videoID=\"yEDU1JqWO70\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Adding and Subtracting Radical Expressions Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Adding and Subtracting Radical Expressions\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_yEDU1JqWO70:hover {cursor:pointer;} img#videoThumbnailImage_yEDU1JqWO70 {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/2219-thumbnail-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_yEDU1JqWO70\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_yEDU1JqWO70\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Adding and Subtracting Radical Expressions\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_yEDU1JqWO70\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_yEDU1JqWO70\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_yEDU1JqWO70\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction lhN_Function() {\n  var x = document.getElementById(\"lhN\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"lhN_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"lhN\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_are_Radical_Expressions\" class=\"smooth-scroll\">What are Radical Expressions?<\/a>\n<ul><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_1\" class=\"smooth-scroll\">Example #1<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_2\" class=\"smooth-scroll\">Example #2<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_3\" class=\"smooth-scroll\">Example #3<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_4\" class=\"smooth-scroll\">Example #4<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_5\" class=\"smooth-scroll\">Example #5<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"toc-h2\"><a href=\"#Adding_and_Subtracting_Radical_Expressions_Practice_Questions\" class=\"smooth-scroll\">Adding and Subtracting Radical Expressions Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello! Today we are going to take a look at adding and subtracting radical expressions. A <strong>radical expression<\/strong> is any expression that includes a radical, or a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/roots\/\">root<\/a>.<\/p>\n<h2><span id=\"What_are_Radical_Expressions\" class=\"m-toc-anchor\"><\/span>What are Radical Expressions?<\/h2>\n<p>\nFor example, some radical expressions are:<\/p>\n<div class=\"examplesentence\">\\(4\\sqrt{2}, \\sqrt{x+5}, \\text{ and } \\sqrt[3]{39}\\)<\/div>\n<p>\n&nbsp;<br \/>\nRadical expressions can include numbers, variables, and fractions. For this video, we are going to focus on adding and subtracting simple square root radical expressions, but the same process applies to all radical expressions.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nLet\u2019s start by adding \\(6\\sqrt{3}\\) and \\(2\\sqrt{3}\\).<\/p>\n<div class=\"examplesentence\">\\(6\\sqrt{3}+2\\sqrt{3}\\)<\/div>\n<p>\n&nbsp;<br \/>\nTo add or subtract radical expressions, their radicals must be the same. If they aren\u2019t, then the two terms are not like terms and cannot be added or subtracted.<\/p>\n<p>In this example, our radicals are the same, so we can add their coefficients. \\(6+2=8\\), and our radical stays the same, so our answer is:<\/p>\n<div class=\"examplesentence\">\\(6\\sqrt{3}+2\\sqrt{3}=8\\sqrt{3}\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s try another one.<\/p>\n<div class=\"examplesentence\">\\(14\\sqrt{6}-9\\sqrt{6}\\)<\/div>\n<p>\n&nbsp;<br \/>\nOur radicals are the same for this problem as well, so all we have to do is subtract our coefficients:<\/p>\n<div class=\"examplesentence\">\\(14\\sqrt{6}-9\\sqrt{6}=5\\sqrt{6}\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h3>\n<p>\nBut, what if we&#8217;re asked to solve something like \\(25\\sqrt{3}+6\\sqrt{27}\\)?<\/p>\n<p>At first glance, it doesn&#8217;t look like this is possible because our radicals are not the same, but it turns out it is possible. All we have to do is simplify our second term. So, let&#8217;s look at this one for a second. We&#8217;re going to take a look at \\(6\\sqrt{27}\\), specifically the root right here. <\/p>\n<p>What if we write this as, \\(6\\sqrt{9\\times 3}\\), because \\(9\\times 3=27\\). So we break our 27 apart into <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/factors\/\">factors<\/a>.<\/p>\n<div class=\"examplesentence\">\\(6\\sqrt{27}=6\\sqrt{9\\times 3}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWe know that 9 is a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/square-root-and-perfect-square\/\">perfect square<\/a>, so we can pull this out of the square root and multiply it by our original coefficient. So we can do \\(3\\times 6\\), because \\(\\sqrt{9}=3\\), so make sure you don&#8217;t multiply by 9, but you multiply by \\(\\sqrt{9}\\). <\/p>\n<div class=\"examplesentence\">\\(3\\times 6\\sqrt{3}=18\\sqrt{3}\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo now we can rewrite this problem as:<\/p>\n<div class=\"examplesentence\">\\(25\\sqrt{3}+18\\sqrt{3}\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow our radicals are the same, and we can simply add our coefficients.<\/p>\n<div class=\"examplesentence\">\\(25\\sqrt{3}+18\\sqrt{3}=43\\sqrt{3}\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Example_4\" class=\"m-toc-anchor\"><\/span>Example #4<\/h3>\n<p>\nNow let&#8217;s take a look at a subtraction problem.<\/p>\n<div class=\"examplesentence\">\\(8\\sqrt{32}-2\\sqrt{8}\\)<\/div>\n<p>\n&nbsp;<br \/>\nOur radicals are not the same, so we need to start by simplifying them. In this case, both our radicals can be simplified. So let&#8217;s start with \\(8\\sqrt{32}\\). We can break 32 apart into the factors 16 and 2, so we can write this as:<\/p>\n<div class=\"examplesentence\">\\(8\\sqrt{32}=8\\sqrt{16\\times 2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWe can pull our 16 out because that&#8217;s a perfect square, the square root of 16 is 4, so we&#8217;ll have:<\/p>\n<div class=\"examplesentence\">\\(8\\sqrt{16\\times 2}=4\\times 8\\sqrt{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd then \\(4\\times 8=32\\), so we have \\(32\\sqrt{2}\\).<\/p>\n<div class=\"examplesentence\">\\(8\\sqrt{32}=32\\sqrt{2}\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Example_5\" class=\"m-toc-anchor\"><\/span>Example #5<\/h3>\n<p>\nNow let&#8217;s take a look at \\(2\\sqrt{8}\\). \\(\\sqrt{8}\\) can be rewritten as \\(\\sqrt{4\\times 2}\\), so we&#8217;ll have \\(2\\sqrt{4\\times 2}\\).<\/p>\n<div class=\"examplesentence\">\\(2\\sqrt{8}=2\\sqrt{4\\times 2}\\)<\/div>\n<p>\n&nbsp;<br \/>\n4 is a perfect square, so we can square root this and get 2, and then we&#8217;ll multiply 2 times \\(2\\sqrt{2}\\).<\/p>\n<div class=\"examplesentence\">\\(2\\sqrt{4\\times 2}=2\\times 2\\sqrt{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\n\\(2\\times 2=4\\), so this is equal to \\(4\\sqrt{2}\\).<\/p>\n<div class=\"examplesentence\">\\(2\\sqrt{8}=4\\sqrt{2}\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<br \/>\nAnd now we can subtract! So, we&#8217;ll take our \\(8\\sqrt{32}\\), which became \\(32\\sqrt{2}\\), minus our \\(2\\sqrt{8}\\), which became \\(4\\sqrt{2}\\).<\/p>\n<div class=\"examplesentence\">\\(32\\sqrt{2}-4\\sqrt{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd we subtract our coefficients, \\(32-4=28,\\) and our root stays the same. So we have \\(28\\sqrt{2}\\).<\/p>\n<div class=\"examplesentence\">\\(32\\sqrt{2}-4\\sqrt{2}=28\\sqrt{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd that\u2019s all there is to it! Remember, two radicals must be the same in order to add or subtract their coefficients. I hope this video was helpful. Thanks for watching and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Adding_and_Subtracting_Radical_Expressions_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Adding and Subtracting Radical Expressions Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nThe expression \\(5\\sqrt{6}-8\\sqrt{6}\\) is equivalent to which of the following?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(-\\sqrt{6}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">\\(-3\\sqrt{6}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">\\(3\\sqrt{6}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(2\\sqrt{6}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To combine two or more radical terms, the radicals for each term must be the same. Since both terms contain the radical \\(\\sqrt{6}\\), we can combine their coefficients to get \\(5-8=-3\\). The radical portion of the result stays the same, so our answer is \\(-3\\sqrt{6}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nThe expression \\(4\\sqrt{5}+2\\sqrt{45}\\) is equivalent to which of the following?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\\(6\\sqrt{50}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(38\\sqrt{45}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-3\">\\(10\\sqrt{5}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">The expression does not simplify.<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To combine two or more radical terms, the radicals for each term must be the same. The two radical terms do not contain the same radical. So, simplify the second term.<\/p>\n<p style=\"text-align: center; line-height: 40px\">\\(2\\sqrt{45}=2\\times\\sqrt{9\\times5}=2\\times\\sqrt9\\times\\sqrt5\\)\\(\\:=2\\times3\\times\\sqrt5=6\\sqrt5\\)<\/p>\n<p>Now, we have \\(4\\sqrt{5}+6\\sqrt{5}\\). Since both expressions now contain the radical \\(\\sqrt{5}\\), we can combine their coefficients to get [\/latex]4+6=10[\/latex]. The radical portion of the result stays the same, so our answer is \\(10\\sqrt{5}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nThe expression \\(5\\sqrt{63}+2\\sqrt{28}\\) is equivalent to which of the following?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-3-1\">\\(19\\sqrt{7}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(7\\sqrt{91}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(34\\sqrt{63}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">The expression does not simplify.<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To combine two or more radical terms, the radicals for each term must be the same. The two radical terms do not contain the same radical. So, simplify each term.<\/p>\n<p class=\"longmath\" style=\"text-align: center; line-height: 40px\">\\(5\\sqrt{63}=5\\times\\sqrt{9\\times7}=5\\times\\sqrt{9}\\times\\sqrt{7}=5\\times3\\times\\sqrt{7}=15\\sqrt{7}\\)<br \/>\n\\(2\\sqrt{28}=2\\times\\sqrt{4\\times7}=2\\times\\sqrt{4}\\times\\sqrt{7}=2\\times2\\times\\sqrt{7}=4\\sqrt{7}\\)<\/p>\n<p>Now, we have \\(15\\sqrt{7}+4\\sqrt{7}\\). Since both terms now contain the radical \\(\\sqrt{7}\\), we can combine their coefficients to get \\(15+4=19\\). The radical portion of the result stays the same, so our answer is \\(\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nA garden is in the shape of a rectangle. If the length of the garden is \\(30\\sqrt{10}\\text{ feet}\\) and the width is \\(11\\sqrt{40}\\text{ feet}\\), how much fence will be needed, in feet, to enclose the garden?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\(52\\sqrt{10}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-2\">\\(104\\sqrt{10}\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(82\\sqrt{50}\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(41\\sqrt{50}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To find out how much fence is needed to enclose the rectangular garden, we need to find the perimeter of garden. Use the formula for finding the perimeter, \\(P\\), of a rectangle (where \\(l\\) is the length, and \\(w\\) is the width of the rectangle). <\/p>\n<p style=\"text-align: center;\">\\(P=2l+2w\\) or \\(P=l+l+w+w\\)<\/p>\n<p>Since the length is \\(30\\sqrt{10}\\) feet and the width is \\(11\\sqrt{40}\\) feet, we have:<\/p>\n<p class=\"longmath\" style=\"text-align: center;\">\\(P=30\\sqrt{10}+30\\sqrt{10}+11\\sqrt{40}+11\\sqrt{40}\\)<\/p>\n<p>To combine two or more radical terms, the radicals for each term must be the same. The radical terms do not all contain the same radical. So, simplify the width.<\/p>\n<p style=\"text-align: center; line-height: 40px\">\\(11\\sqrt{40}\\)\\(\\:=11\\times\\sqrt{4\\times10}=11\\times\\sqrt4\\times\\sqrt{10}\\)\\(\\:=11\\times2\\times\\sqrt{10}\\)\\(\\:=22\\sqrt{10}\\)<\/p>\n<p>Now, we have:<\/p>\n<p class=\"longmath\" style=\"text-align: center;\">\\(P=30\\sqrt{10}+30\\sqrt{10}+22\\sqrt{10}+22\\sqrt{10}\\)<\/p>\n<p>Since each term now contains the radical \\(\\sqrt{10}\\), we can combine their coefficients to get:<\/p>\n<p style=\"text-align: center;\">\\(30+30+22+22=104\\)<\/p>\n<p>The radical portion of the result stays the same, so the perimeter is \\(104\\sqrt{10}\\text{ feet}\\). This means \\(104\\sqrt{10}\\text{ feet}\\) of fence is needed to enclose the garden.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nYour friend calculates the distances you run on two consecutive days. The first day you ran \\(3\\sqrt8\\text{ miles}\\), and the second day you ran \\(\\sqrt{50}\\text{ miles}\\). What is the total number of miles you ran on both days?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(14\\sqrt{2}\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(4\\sqrt{58}\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">\\(3\\sqrt{58}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-4\">\\(11\\sqrt{2}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To find the total distance you ran, you need to combine the distance ran for both days:<\/p>\n<p style=\"text-align: center;\">\\(3\\sqrt{8}+\\sqrt{50}\\)<\/p>\n<p>To combine two or more radical terms, the radicals for each term must be the same. The two radical terms do not contain the same radical. So, simplify each term.<\/p>\n<p class=\"longmath\" style=\"text-align: center; line-height: 40px\">\\(3\\sqrt{8}=3\\times\\sqrt{4\\times2}=3\\times\\sqrt{4}\\times\\sqrt{2}=3\\times2\\times\\sqrt{4}=6\\sqrt{2}\\)<br \/>\n\\(\\sqrt{50}=\\sqrt{25\\times2}=\\sqrt{25}\\times\\sqrt{2}=5\\sqrt{2}\\)<\/p>\n<p>Now, we have \\(6\\sqrt{2}+5\\sqrt{2}\\) Since both expressions now contain \\(\\sqrt{2}\\), we can combine their coefficients to get \\(6+5=11\\). The radical portion of the result stays the same, so you ran a total of \\(11\\sqrt{2}\\text{ miles}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/algebra-i\/\">Return to Algebra I Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Algebra I Videos<\/p>\n","protected":false},"author":22,"featured_media":116189,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-116180","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-practice-question-videos","7":"page_type-video","8":"content_type-practice-questions","9":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/116180","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=116180"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/116180\/revisions"}],"predecessor-version":[{"id":281132,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/116180\/revisions\/281132"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/116189"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=116180"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}