{"id":4022,"date":"2023-02-01T06:54:00","date_gmt":"2023-02-01T06:54:00","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=4022"},"modified":"2023-02-01T06:54:00","modified_gmt":"2023-02-01T06:54:00","slug":"ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-2","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-2\/","title":{"rendered":"NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.2"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 9 Maths\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 1 (Number Systems )\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 9 Mathematics\u00a0<strong>Chapter &#8211; 1 Number Systems\u00a0<\/strong>Exercise 1.2 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Chapter 1: Number Systems<\/strong><\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-1\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 1.1<\/a><\/li>\n<li><span style=\"color: #000000;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-3\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 1.3<\/a><\/span><\/li>\n<li><span style=\"color: #000000;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-4\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 1.4<\/a><\/span><\/li>\n<li><span style=\"color: #000000;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 1.5<\/a><\/span><\/li>\n<li><span style=\"color: #000000;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-6\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 1.6<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 1.2\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. State whether the following statements are true or false. Justify your answers.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(i)<\/strong> Every irrational number is a real number.<br \/>\n<strong>(ii) <\/strong>Every point on the number line is of the form \u221am where m is a natural number.<br \/>\n<strong>(iii)<\/strong> Every real number is an irrational number.<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">Answer &#8211;<br \/>\n<\/span><\/strong><span style=\"color: #000000;\"><strong>(i)<\/strong> Every irrational number is a real number. <strong>(True)<br \/>\n<\/strong>\u2235 Real numbers = Rational numbers + Irrational numbers.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) <\/strong>Every point on the number line is of the form \u221am where m is a natural number. <strong>(False)<br \/>\n<\/strong>\u2235 no negative number can be the square root of any natural number.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii)<\/strong> Every real number is an irrational number. <strong>(False)<br \/>\n<\/strong><\/span>\u2235 rational numbers are also present in the set of real numbers.<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.<\/strong><br \/>\n<\/span><strong><span style=\"color: #000000;\">Answer &#8211;\u00a0<\/span><\/strong><span style=\"color: #000000;\">No, the square roots of all positive integers are not irrational.<br \/>\n<\/span><span style=\"color: #000000;\">For example,<br \/>\n<\/span><span style=\"color: #000000;\">\u221a4 = 2 is rational.<br \/>\n<\/span><span style=\"color: #000000;\">\u221a9 = 3 is rational.<br \/>\n<\/span><span style=\"color: #000000;\">Hence, the square roots of positive integers 4 and 9 are not irrational.\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. Show how\u00a0\u221a5\u00a0can be represented on the number line.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4184\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.2-Q3.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"347\" height=\"153\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.2-Q3.png 347w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.2-Q3-300x132.png 300w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><\/strong><br \/>\n<\/span><span style=\"color: #000000;\"><strong>Step 1 &#8211;<\/strong> Let line OQ be of 2 unit on a number line.<br \/>\n<\/span><span style=\"color: #000000;\"><strong>Step 2 &#8211;<\/strong>\u00a0At Q, draw a perpendicular line QP of length 1 unit.<br \/>\n<\/span><span style=\"color: #000000;\"><strong>Step 3 &#8211;<\/strong> Join OP<br \/>\n<\/span><span style=\"color: #000000;\"><strong>Step 4 &#8211;<\/strong>\u00a0Now, OPQ is a right angled triangle. Applying Pythagoras theorem,<br \/>\n<\/span><span style=\"color: #000000;\">OQ<sup>2 <\/sup>+ QP<sup>2<\/sup> = OP<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">2<sup>2 <\/sup>+ 1<sup>2<\/sup> = OP<sup>2<\/sup><br \/>\nOP<sup>2<\/sup> = 5<br \/>\n<\/span><span style=\"color: #000000;\">\u21d2 OP = \u221a5 .<br \/>\nThus, OP is a line of length \u221a5 unit.<br \/>\nNow, take O as centre OP = \u221a5 as radius, draw an arc, which intersects the line at point R.<br \/>\nHence, the point R represents \u221a5.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. Classroom activity (Constructing the \u2018square root spiral\u2019) : Take a large sheet of paper and construct the \u2018square root spiral\u2019 in the following fashion. Start with a point O and draw a line segment OP<sub>1<\/sub> of unit length. Draw a line segment P<sub>1<\/sub>P<sub>2<\/sub> perpendicular to OP<sub>1<\/sub>\u00a0of unit length (see Fig. 1.9). Now draw a line segment P<sub>2<\/sub>P<sub>3<\/sub>\u00a0perpendicular to OP<sub>2<\/sub>. Then draw a line segment P<sub>3<\/sub>P<sub>4<\/sub>\u00a0perpendicular to OP<sub>3<\/sub>. Continuing in Fig. 1.9 :<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4185\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.2-Q4.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"271\" height=\"211\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Constructing this manner, you can get the line segment P<sub>n-1<\/sub>P<sub>n<\/sub> by square root spiral drawing a line segment of unit length perpendicular to OP<sub>n-1<\/sub>. In this manner, you will have created the points P<sub>2<\/sub>, P<sub>3<\/sub>,\u2026.,P<sub>n<\/sub>,\u2026 ., and joined them to create a beautiful spiral depicting \u221a2, \u221a3, \u221a4, \u2026<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>Answer &#8211;<\/strong><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4186\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.2-Ans4.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"644\" height=\"518\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.2-Ans4.png 644w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.2-Ans4-300x241.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.2-Ans4-480x386.png 480w\" sizes=\"auto, (max-width: 644px) 100vw, 644px\" \/><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Step 1 &#8211; <\/strong>Mark a point O on the paper. Here, O will be the center of the square root spiral.<br \/>\n<\/span><span style=\"color: #000000;\"><strong>Step 2<\/strong> <strong>&#8211;<\/strong> From O, draw a straight line, OA, of 1cm horizontally.<br \/>\n<\/span><span style=\"color: #000000;\"><strong>Step 3<\/strong> <strong>&#8211;<\/strong> From A, draw a perpendicular line, AB, of 1 cm.<br \/>\n<\/span><span style=\"color: #000000;\"><strong>Step 4 &#8211;<\/strong> Join OB. Here, OB will be of \u221a2<br \/>\n<\/span><span style=\"color: #000000;\"><strong>Step 5 &#8211;<\/strong> Now, from B, draw a perpendicular line of 1 cm and mark the end point C.<br \/>\n<\/span><span style=\"color: #000000;\"><strong>Step 6 &#8211;<\/strong> Join OC. Here, OC will be of \u221a3<br \/>\n<\/span><span style=\"color: #000000;\"><strong>Step 7 &#8211;<\/strong> Repeat the steps to draw \u221a4, \u221a5, \u221a6\u2026.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 9 Maths\u00a0 Chapter &#8211; 1 (Number Systems )\u00a0 The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter &#8211; 1 Number Systems\u00a0Exercise 1.2 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 1: Number Systems NCERT Solution Class 9 Maths Ex &#8211; 1.1 NCERT Solution [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[698],"tags":[699,702,186,700,701,5],"class_list":["post-4022","post","type-post","status-publish","format-standard","hentry","category-class-9-maths","tag-class-9th-chapter-1-number-systems-in-english","tag-ncert-solution-class-9","tag-ncert-solutions","tag-ncert-solutions-class-9-maths-chapter-1-in-english","tag-ncert-solutions-class-9-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.5) - 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