{"id":323,"date":"2020-09-07T09:33:05","date_gmt":"2020-09-07T04:03:05","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=323"},"modified":"2021-07-02T15:03:45","modified_gmt":"2021-07-02T09:33:45","slug":"kseeb-solutions-class-9-maths-chapter-1-ex-1-5","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/kseeb-solutions-class-9-maths-chapter-1-ex-1-5\/","title":{"rendered":"KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5"},"content":{"rendered":"

KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5<\/strong> are part of KSEEB Solutions for Class 9 Maths<\/a>. Here we have given Karnataka Board Class 9 Maths Chapter 1 Number Systems Exercise 1.5.<\/p>\n

Karnataka Board Class 9 Maths Chapter 1 Number Systems Ex 1.5<\/h2>\n

Question 1.
\nClassify the following numbers as rational or irrational.
\nAnswer:
\ni) \\(2-\\sqrt{5}\\)
\nii) \\((3+\\sqrt{23})-\\sqrt{23}\\)
\niii) \\(\\frac{2 \\sqrt{7}}{7 \\sqrt{7}}\\)
\niv) \\(\\frac{1}{\\sqrt{2}}\\)
\nv) 2\u03c0
\nAnswer:
\ni) \\(2-\\sqrt{5}\\) = 2 – 2.2360679……….. = -0.2360679
\nThis is a non-terminating, non-recurring decimal.
\n\u2234 This is an irrational number.<\/p>\n

ii) \\((3+\\sqrt{23})-\\sqrt{23}\\)
\n= \\(3+\\sqrt{23}-\\sqrt{23}\\)
\n= 3
\n\u21d2 \\(\\frac{3}{1}\\). This can be written in the form of \\(\\frac{p}{q}\\).
\n\u2234 This is a rationl number.<\/p>\n

iii) \\(\\frac{2 \\sqrt{7}}{7 \\sqrt{7}}=\\frac{2 \\sqrt{7}}{\\sqrt{7}}=2 \\Rightarrow \\frac{2}{1}\\)
\nThis can be written in the form of \\(\\frac{p}{q}\\)
\n\u2234 This is a rational number.<\/p>\n

iv) \\(\\frac{1}{\\sqrt{2}}\\)
\n\\(\\frac{1}{\\sqrt{2}} \\times \\frac{\\sqrt{2}}{\\sqrt{2}}=\\frac{\\sqrt{2}}{2}=\\frac{1.4142}{2}\\)
\n= 0.707106…………
\nThis is a non-terminating, non-recurring decimal.
\n\u2234 This is an irrational number.<\/p>\n

v) 2\u03c0
\n= 2 \u00d7 3.1415…..
\n= 6.2830…….
\nThis is a non-terminating, non-recurring decimal.
\n\u2234 This is an irrational number.<\/p>\n

Question 2.
\nSimplify each of the following expressions:
\ni) \\((3+\\sqrt{3})(2+\\sqrt{2})\\)
\nii) \\((3+\\sqrt{3})(3-\\sqrt{3})\\)
\niii) \\((\\sqrt{5}+\\sqrt{2})^{2}\\)
\niv) \\((\\sqrt{5}-\\sqrt{2})(\\sqrt{5}+\\sqrt{2})\\)
\nAnswer:
\n\"KSEEB
\n\"KSEEB<\/p>\n

Question 3.
\nRecall, 2\u03c0 is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, \\(\\pi=\\frac{c}{d}\\). This seems to contradict the fact that n is irrational. How will you resolve this contradiction?
\nAnswer:
\nThere is no contradiction. When we measure a length with a scale or any other device we get the quotient.
\nTherefore we cannot judge whether c is a rational number of d is an irrational number.
\n\u2234 Value of \\(\\frac{c}{d}\\) is irrational number.
\n\u2234 The value of \u03c0 is also an irrational number.<\/p>\n

Question 4.
\nRepresent \\(\\sqrt{9.3}\\) on the number line.
\nAnswer:
\nConstruction: Mark the distance 9.5 units from a fixed point O such that OB = 9.3 units. Mark midpoint D of OC. Draw a semicircle with centre D. Draw a line perpendicular to OC passing through E and intersecting the semicircle at E. Draw an arc BE which intersect at F. Now, BF = \\(\\sqrt{9.3}\\).
\n\"KSEEB<\/p>\n

Question 5.
\nRationalise the denominators of the following :
\n\"KSEEB
\nAnswer:
\ni) \\(\\frac{1}{\\sqrt{7}}\\)
\nDenominator\u2019s factor is \\(\\sqrt{7}\\) Mulitplying Numerator and denominator by \\(\\sqrt{7}\\).
\n\"KSEEB<\/p>\n

ii) \\(\\frac{1}{\\sqrt{7}-\\sqrt{6}}\\)
\nDenominator’s factor is \\(\\sqrt{7}+\\sqrt{6}\\)
\nMultiplying numerator and denominator by \\(\\sqrt{7}+\\sqrt{6}\\),
\n\"KSEEB<\/p>\n

iii) \\(\\frac{1}{\\sqrt{5}+\\sqrt{2}}\\)
\nDenominator’s factor is \\(\\sqrt{5}-\\sqrt{2}\\)
\nMultiplying numerator and denominator by \\(\\sqrt{5}-\\sqrt{2}\\).
\n\"KSEEB<\/p>\n

iv) \\(\\frac{1}{\\sqrt{7}-2}\\)
\nDenominator’s factor is \\(\\sqrt{7}+2\\)
\nMultiplying numerator and denominator by \\(\\sqrt{7}+2\\).
\n\"KSEEB<\/p>\n

We hope the KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 help you. If you have any query regarding Karnataka Board Class 9 Maths Chapter 1 Number Systems Exercise 1.5, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"

KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 are part of KSEEB Solutions for Class 9 Maths. Here we have given Karnataka Board Class 9 Maths Chapter 1 Number Systems Exercise 1.5. Karnataka Board Class 9 Maths Chapter 1 Number Systems Ex 1.5 Question 1. Classify the following numbers as rational …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/323"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=323"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/323\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=323"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=323"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}