{"id":3900,"date":"2023-05-16T12:32:17","date_gmt":"2023-05-16T07:02:17","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=3900"},"modified":"2023-05-17T17:35:31","modified_gmt":"2023-05-17T12:05:31","slug":"ap-board-9th-class-maths-solutions-chapter-1-ex-1-4","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/ap-board-9th-class-maths-solutions-chapter-1-ex-1-4\/","title":{"rendered":"AP Board 9th Class Maths Solutions Chapter 1 Real Numbers Ex 1.4"},"content":{"rendered":"

AP State Syllabus AP Board 9th Class Maths Solutions<\/a> Chapter 1 Real Numbers Ex 1.3 Textbook Questions and Answers.<\/p>\n

AP State Syllabus 9th Class Maths Solutions 1st Lesson Real Numbers Exercise 1.4<\/h2>\n

Question 1.
\nSimple the following expressions.
\ni) (5 + \u221a7) (2 + \u221a5)
\nSolution:
\n(5 + \u221a7) (2 + \u221a5)
\n= 10 + 5\u221a5 + 2\u221a7 + \u221a35<\/p>\n

ii) (5 + \u221a5) (5 – \u221a5)
\nSolution:
\n(5 + \u221a5) (5 – \u221a5)
\n= 52<\/sup> + (\u221a5)2<\/sup>
\n= 25 – 5 = 20<\/p>\n

\"AP<\/p>\n

(iii) (\u221a3 + \u221a7)2<\/sup>
\nSolution:
\n(\u221a3 + \u221a7)2<\/sup>
\n= (\u221a3)2<\/sup> + (\u221a7)2<\/sup> + 2(\u221a3)(\u221a7)
\n= 3 + 7 + 2\u221a21
\n= 10 + 2\u221a21<\/p>\n

iv) (\u221a11 – \u221a7) (\u221a11 + \u221a7)
\n= (\u221a11)2<\/sup> – (\u221a7)2<\/sup>
\n= 11 – 7 = 4<\/p>\n

Question 2.
\nClassify the following numbers as rational or irrational.
\ni) 5 – \u221a3
\nii) \u221a3 + \u221a2
\niii) (\u221a2 – 2)2<\/sup>
\niv) \\(\\frac{2 \\sqrt{7}}{7 \\sqrt{7}}\\)
\nv) 2\u03c0
\nvii) (2 +\u221a2) (2 – \u221a2)
\nSolution:
\ni) 5 – \u221a3 – irrational
\nii) \u221a3 + \u221a2 – irrational
\niii) (\u221a2 – 2)2<\/sup> – irrational
\niv) \\(\\frac{2 \\sqrt{7}}{7 \\sqrt{7}}\\) – rational
\nv) 2\u03c0 – Transcendental number. (not irrational)
\nvi) \\(\\frac{1}{\\sqrt{3}}\\)– irrational
\nvii) (2 +\u221a2) (2 – \u221a2) – rational<\/p>\n

\"AP<\/p>\n

Question 3.
\nIn the following equations, find whether variables x, y, z etc., represents rational or irrational numbers.
\ni) x2<\/sup> = 7
\nii) y2<\/sup> = 16
\niii) z2<\/sup> = 0.02
\niv) u2<\/sup> = \\(\\frac{17}{4}\\)
\nv) w2<\/sup> = 27
\nvi) t4<\/sup> = 256
\nSolution:
\ni) x2<\/sup> = 7
\n\u21d2 x = \u221a7 is an irrational number.
\nii) y2<\/sup> = 16 \u21d2 y = 4 is a rational number.
\niii) z2<\/sup> = 0.02 \u21d2 z = \\(\\sqrt{0.02}\\) is an irrational number.
\niv) u2<\/sup> = \\(\\frac{17}{4}\\) \u21d2 x = \\(\\frac{\\sqrt{17}}{2}\\) is an irrational number.
\nv) w2<\/sup> = 27 \u21d2 w = \\(3 \\sqrt{3}\\) an irrational number.
\nvi) t4<\/sup> = 256 \u21d2 t2<\/sup> = \\(\\sqrt{256}\\) = 16
\n\u21d2 t = \\(\\sqrt{16}\\) = 4 is a rational number<\/p>\n

Qeustion 4.
\nThe ratio of circumference to the diameter of a circle c\/d is represented by \u03c0. But we say that \u03c0 is an irrational number. Why?<\/p>\n

Question 5.
\nRationalise the denominators of the following.
\ni) \\(\\frac{1}{3+\\sqrt{2}}\\)
\nSolution:
\n\"AP<\/p>\n

ii) \\(\\frac{1}{\\sqrt{7}-\\sqrt{6}}\\)
\nSolution:
\n\"AP<\/p>\n

iii) \\(\\frac{1}{\\sqrt{7}}\\)
\nSolution:
\n\"AP<\/p>\n

\"AP<\/p>\n

iv) \\(\\frac{\\sqrt{6}}{\\sqrt{3}-\\sqrt{2}}\\)
\nSolution:
\n\"AP
\n\"AP<\/p>\n

Question 6.
\nSimplify each of the following by rationalising the denominator.
\ni) \\(\\frac{6-4 \\sqrt{2}}{6+4 \\sqrt{2}}\\)
\nSolution:
\n\"AP<\/p>\n

ii) \\(\\frac{\\sqrt{7}-\\sqrt{5}}{\\sqrt{7}+\\sqrt{5}}\\)
\nSolution:
\n\"AP<\/p>\n

iii) \\(\\frac{1}{3 \\sqrt{2}-2 \\sqrt{3}}\\)
\nSolution:
\n\"AP<\/p>\n

iv) \\(\\frac{3 \\sqrt{5}-\\sqrt{7}}{3 \\sqrt{3}+\\sqrt{2}}\\)
\nSolution:
\n\"AP<\/p>\n

Question 7.
\nFind the value of \\(\\frac{\\sqrt{10}-\\sqrt{5}}{2 \\sqrt{2}}\\) upto three decimal places. (take \\(\\sqrt{2}\\) = 1.414, \\(\\sqrt{3}\\) = 1.732 and \\(\\sqrt{5}\\) = 2.236).
\nSolution:
\n\"AP
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 8.
\nFind
\ni) 641\/6<\/sup>
\nSolution:
\n= (26<\/sup>)1\/6<\/sup>
\n= 6<\/p>\n

ii) 321\/5<\/sup>
\nSolution:
\n321\/5<\/sup>
\n= (25<\/sup>)1\/5<\/sup>
\n= 2<\/p>\n

iii) 6251\/4<\/sup>
\n6251\/5<\/sup>
\n= (54<\/sup>)1\/4<\/sup>
\n= 5<\/p>\n

iv) 163\/2<\/sup>
\nSolution:
\n163\/2<\/sup>
\n= (42<\/sup>)3\/2<\/sup><\/p>\n

v) 2432\/5<\/sup>
\nSolution:
\n2432\/5<\/sup>
\n= (35<\/sup>)2\/5<\/sup><\/p>\n

vi) (46656)-1\/6<\/sup>
\nSolution:
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 9.
\nSimplify \\(\\sqrt[4]{81}-8 \\sqrt[3]{343}+15 \\sqrt[5]{32}+\\sqrt{225}\\)
\nSolution:
\n\"AP<\/p>\n

Question 10.
\nIf ‘a’ and ‘b’ are rational numbers, find the values of a and b in each of the following equations.
\ni) \\(\\frac{\\sqrt{3}+\\sqrt{2}}{\\sqrt{3}-\\sqrt{2}}=\\mathbf{a}+\\mathbf{b} \\sqrt{6}\\)
\nSolution:
\nGiven that \\(\\frac{\\sqrt{3}+\\sqrt{2}}{\\sqrt{3}-\\sqrt{2}}=\\mathbf{a}+\\mathbf{b} \\sqrt{6}\\)
\nRationalising the denominator we get
\n\"AP
\nComparing 5 + 2\u221a6 with a + b\u221a6
\nWe have a = 5 and b = 2<\/p>\n

\"AP<\/p>\n

ii) \\(\\frac{\\sqrt{5}+\\sqrt{3}}{2 \\sqrt{5}-3 \\sqrt{3}}=a-b \\sqrt{15}\\)
\nSolution:
\nGiven that \\(\\frac{\\sqrt{5}+\\sqrt{3}}{2 \\sqrt{5}-3 \\sqrt{3}}=a-b \\sqrt{15}\\)
\nRationalising the denominator we get
\n\"AP<\/p>\n

AP Board 9th Class Maths Solutions<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus AP Board 9th Class Maths Solutions Chapter 1 Real Numbers Ex 1.3 Textbook Questions and Answers. AP State Syllabus 9th Class Maths Solutions 1st Lesson Real Numbers Exercise 1.4 Question 1. Simple the following expressions. i) (5 + \u221a7) (2 + \u221a5) Solution: (5 + \u221a7) (2 + \u221a5) = 10 + … Read more<\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/3900"}],"collection":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/comments?post=3900"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/3900\/revisions"}],"predecessor-version":[{"id":40512,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/3900\/revisions\/40512"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/media?parent=3900"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/categories?post=3900"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/tags?post=3900"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}