{"id":8116,"date":"2023-09-20T17:47:30","date_gmt":"2023-09-20T17:47:30","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=8116"},"modified":"2025-08-28T04:01:40","modified_gmt":"2025-08-28T04:01:40","slug":"irrational-numbers-apply-it-1","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/irrational-numbers-apply-it-1\/","title":{"raw":"Irrational Numbers: Apply It 1","rendered":"Irrational Numbers: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Recognize irrational numbers in a list of numbers<\/li>\r\n\t<li>Simplify irrational numbers to their lowest terms<\/li>\r\n\t<li>Add, subtract, multiple and divide irrational numbers<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Unraveling the Irrational: A Cosmic Calculation Challenge<\/h2>\r\n<p>Sam is an aspiring astronomer working on a school project to map out constellations. The project involves using measurements that often result in irrational numbers, such as distances between stars in light-years that are not whole numbers. Your task is to help Sam calculate these distances and create a scale model of a constellation.<\/p>\r\n<center>\r\n[caption id=\"attachment_10393\" align=\"aligncenter\" width=\"500\"]<img class=\"wp-image-10393 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/06185217\/pexels-photo-1906658-1.jpeg\" alt=\"A starry night sky\" width=\"500\" height=\"500\" \/> Figure 1. Help Sam calculate distances and create a scale model of a constellation[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>Sam has a list of distances between stars, some of which are irrational. Help Sam identify which of these are irrational numbers: [latex]\\sqrt{2}, \\sqrt{16}, \\pi, \\frac{22}{7}, \\sqrt{81}, \\sqrt{23}[\/latex].<\/p>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13850[\/ohm2_question]<\/p>\r\n<\/section>\r\n<p>The distance to a nearby star is [latex]10\\sqrt{2}[\/latex] light-years. Another star is [latex]3\\sqrt{2}[\/latex] light-years further than the first. What is the total distance to the second star?<\/p>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13852[\/ohm2_question]<\/p>\r\n<\/section>\r\n<p>Sam wonders how many times farther away the second star is compared to the distance between Earth and the Moon, which is approximately [latex]1.28\\sqrt{2}[\/latex] light-years.<\/p>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13853[\/ohm2_question]<\/p>\r\n<\/section>\r\n<p>For the scale model, Sam needs to convert the actual light-year distances into centimeters. If [latex]\\sqrt{2}[\/latex] light-years is represented by [latex]1[\/latex] cm, what is the model distance for these two stars that is?<\/p>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13856[\/ohm2_question]<\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Recognize irrational numbers in a list of numbers<\/li>\n<li>Simplify irrational numbers to their lowest terms<\/li>\n<li>Add, subtract, multiple and divide irrational numbers<\/li>\n<\/ul>\n<\/section>\n<h2>Unraveling the Irrational: A Cosmic Calculation Challenge<\/h2>\n<p>Sam is an aspiring astronomer working on a school project to map out constellations. The project involves using measurements that often result in irrational numbers, such as distances between stars in light-years that are not whole numbers. Your task is to help Sam calculate these distances and create a scale model of a constellation.<\/p>\n<div style=\"text-align: center;\">\n<figure id=\"attachment_10393\" aria-describedby=\"caption-attachment-10393\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-10393 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/06185217\/pexels-photo-1906658-1.jpeg\" alt=\"A starry night sky\" width=\"500\" height=\"500\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/06185217\/pexels-photo-1906658-1.jpeg 500w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/06185217\/pexels-photo-1906658-1-300x300.jpeg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/06185217\/pexels-photo-1906658-1-150x150.jpeg 150w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/06185217\/pexels-photo-1906658-1-65x65.jpeg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/06185217\/pexels-photo-1906658-1-225x225.jpeg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/06185217\/pexels-photo-1906658-1-350x350.jpeg 350w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-10393\" class=\"wp-caption-text\">Figure 1. Help Sam calculate distances and create a scale model of a constellation<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Sam has a list of distances between stars, some of which are irrational. Help Sam identify which of these are irrational numbers: [latex]\\sqrt{2}, \\sqrt{16}, \\pi, \\frac{22}{7}, \\sqrt{81}, \\sqrt{23}[\/latex].<\/p>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13850\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13850&theme=lumen&iframe_resize_id=ohm13850&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<p>The distance to a nearby star is [latex]10\\sqrt{2}[\/latex] light-years. Another star is [latex]3\\sqrt{2}[\/latex] light-years further than the first. What is the total distance to the second star?<\/p>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13852\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13852&theme=lumen&iframe_resize_id=ohm13852&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<p>Sam wonders how many times farther away the second star is compared to the distance between Earth and the Moon, which is approximately [latex]1.28\\sqrt{2}[\/latex] light-years.<\/p>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13853\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13853&theme=lumen&iframe_resize_id=ohm13853&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<p>For the scale model, Sam needs to convert the actual light-year distances into centimeters. If [latex]\\sqrt{2}[\/latex] light-years is represented by [latex]1[\/latex] cm, what is the model distance for these two stars that is?<\/p>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13856\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13856&theme=lumen&iframe_resize_id=ohm13856&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n","protected":false},"author":15,"menu_order":23,"template":"","meta":{"_candela_citation":"[{\"type\":\"pd\",\"description\":\"Silhouette Photography Of Person Under Starry Sky\",\"author\":\" egil sju00f8holt\",\"organization\":\"Pexels\",\"url\":\"https:\/\/www.pexels.com\/photo\/silhouette-photography-of-person-under-starry-sky-1906658\/\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":53,"module-header":"apply_it","content_attributions":[{"type":"pd","description":"Silhouette Photography Of Person Under Starry Sky","author":" egil sju00f8holt","organization":"Pexels","url":"https:\/\/www.pexels.com\/photo\/silhouette-photography-of-person-under-starry-sky-1906658\/","project":"","license":"arr","license_terms":""}],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8116"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":14,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8116\/revisions"}],"predecessor-version":[{"id":15811,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8116\/revisions\/15811"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/53"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8116\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=8116"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=8116"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=8116"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=8116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}