{"id":5910,"date":"2022-01-28T18:29:46","date_gmt":"2022-01-28T18:29:46","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=5910"},"modified":"2022-02-28T18:49:41","modified_gmt":"2022-02-28T18:49:41","slug":"estimating-roots-word-problems","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/estimating-roots-word-problems\/","title":{"rendered":"Estimating Roots Word Problems"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Estimating Roots Word Problems<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Square root of a number is an inverse operation of squaring a number. The square of a number is the value of power 2 of the number, while the square root of a number is the number that we need to multiply by itself to get the original number. If ‘a’ is the square root of ‘b’, it means that a \u00d7 a = b. The square of any number is always a positive number, so every number has two square roots, one positive value, and one negative value. For example, both 2 and -2 are square roots of 4.<\/p>\n<p>Whenever a number (x) is multiplied three times, then the resultant number is known as the cube of that number. Thus, the cube for the number (x) becomes x<sup>3<\/sup> or x-cubed. While on the other hand, the cube root of a number is the reverse process of the cube of a number and is denoted by \u221b.<\/p>\n<p>Estimation and approximation refer to a reasonable guess of the actual value to make calculations easier and realistic. This method helps in estimating and approximating the square root of a given number.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]1. Read the word problem and set up an equation.<br \/>\n2. Isolate the variable, by taking the square root\/cube root of both sides of the equation.<br \/>\n3. Find the largest perfect square\/cube less than the given value.<br \/>\n4. Find the smallest perfect square\/cube greater than the given value.<br \/>\n5. Find which perfect square\/cube the original value is closer to.<br \/>\n6. Calculate the square root\/ cube root of the nearest perfect square\/cube the original value is closer to.[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<span style=\"color: #16a085;\"><strong>The volume of a cube is 350 cm<sup>3<\/sup>. Estimate the length of one side of the cube.<\/strong><\/span><br \/>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]To find the length of one side, you have to find the cube root of 350. 350 is between the perfect cubes 343 and 512. It is closer to 343. The cube root of 343 is 7. So,<\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\sqrt[3]{350}\\approx&space;7\" alt=\"\\fn_phv \\sqrt[3]{350}\\approx 7\" align=\"absmiddle\" \/><\/p>\n<p><strong>The length of one side of the cube is approximately <strong><span style=\"color: red;\">7 cm<\/span><\/strong>.<\/strong>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Estimating Roots Word Problems[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><span style=\"color: #16a085;\"><strong>The area of a square is 600 cm<sup>2<\/sup>. Estimate the length of one side of the square. <\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/estimate-roots\"><img loading=\"lazy\" class=\"alignnone wp-image-5912 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/51-1.png\" alt=\"Estimating Roots Word Problems Practice Problem 1\" width=\"121\" height=\"41\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/estimate-roots”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><span style=\"color: #16a085;\"><strong>The area of a square is 260 cm<sup>2<\/sup>. Estimate the length of one side of the square. <\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/estimate-roots\"><img loading=\"lazy\" class=\"alignnone wp-image-5912 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/51-1.png\" alt=\"Estimating Roots Word Problems Practice Problem 2\" width=\"121\" height=\"41\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/estimate-roots”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><span style=\"color: #16a085;\"><strong>The volume of a cube is 710 cm<sup>3<\/sup>. Estimate the length of one side of the cube. <\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/estimate-roots\"><img loading=\"lazy\" class=\"alignnone wp-image-5912 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/51-1.png\" alt=\"Estimating Roots Word Problems Practice Problem 3\" width=\"121\" height=\"41\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/estimate-roots”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]<strong>Estimation<\/strong> – approximating a quantity to the required accuracy.<\/p>\n<p><strong>Square of a number<\/strong>: A square number is a number multiplied by itself.<\/p>\n<p><strong>Cube of a number:<\/strong> A cube number is a number multiplied by itself 3 times.<\/p>\n<p><strong>Square Root:<\/strong> One of the two equal factors of a number. If a<sup>2<\/sup> = b, then a is the square root of b.<\/p>\n<p><strong>Cube Root:<\/strong> One of the three equal factors of a number. If a<sup>3<\/sup> = b, then a is the cube root of b.<\/p>\n<p><strong>Radical Symbol:<\/strong> A symbol used to indicate a positive square root \u221a[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/rational-numbers\"><span style=\"color: #ed5600;\">Rational Numbers<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/powers-and-exponents\"><span style=\"color: #ed5600;\">Powers and Exponents<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/multiply-and-divide-monomials\"><span style=\"color: #ed5600;\">Multiply and Divide Monomials<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/powers-of-monomials\"><span style=\"color: #ed5600;\">Powers of Monomials<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/negative-exponents\"><span style=\"color: #ed5600;\">Negative Exponents<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/roots\"><span style=\"color: #ed5600;\">Roots<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1637576830956{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-right-color: #333399 !important;border-top-color: #333399 !important;border-bottom-color: #333399 !important;border-radius: 35px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/scientific-notation\"><span style=\"color: #333399;\">Scientific Notation<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/computing-with-scientific-notation\"><span style=\"color: #333399;\">Computing with Scientific Notation<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/compare-real-numbers\"><span style=\"color: #333399;\">Compare Real Numbers<\/span><\/a>[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||”][vc_btn title=”Grade 4″ color=”blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F4th-grade%2Fmaths|title:Grade%204%20Math||”][vc_btn title=”Grade 5″ color=”green” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F5th-grade%2Fmaths|title:Grade%205%20Math||”][vc_btn title=”Grade 6″ color=”info” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F6th-grade%2Fmaths|title:Grade%206%20Math||”][vc_btn title=”Grade 7″ color=”vista-blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F7th-grade%2Fmaths|title:Grade%207%20Math||”][vc_btn title=”Grade 8″ color=”mulled-wine” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F8th-grade%2Fmaths|title:Grade%208%20Math||”][\/vc_column_inner][\/vc_row_inner][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Estimation” color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Festimation|title:Estimation||”][vc_btn title=”Exponents and logarithms” color=”blue” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Fexponents-and-logarithms|title:Exponents%20and%20logarithms||”][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Estimating Roots Word Problems [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Square root of a number is an inverse operation of squaring a number. The square of a number is the value of power 2 of the number, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Estimating Roots Word Problems | Oryx Learning<\/title>\n<meta name=\"description\" content=\"Square root of a number is an inverse operation of squaring a number. 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