{"id":6780,"date":"2023-05-25T14:38:12","date_gmt":"2023-05-25T09:08:12","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=6780"},"modified":"2023-05-26T17:13:48","modified_gmt":"2023-05-26T11:43:48","slug":"ap-board-8th-class-maths-solutions-chapter-6-ex-6-5","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/ap-board-8th-class-maths-solutions-chapter-6-ex-6-5\/","title":{"rendered":"AP Board 8th Class Maths Solutions Chapter 6 Square Roots and Cube Roots Ex 6.5"},"content":{"rendered":"

AP State Syllabus AP Board 8th Class Maths Solutions<\/a> Chapter 6 Square Roots and Cube Roots Ex 6.5 Textbook Questions and Answers.<\/p>\n

AP State Syllabus 8th Class Maths Solutions 6th Lesson Square Roots and Cube Roots Exercise 6.5<\/h2>\n

\"AP<\/p>\n

Question 1.
\nFind the cube root of the following numbers by prime factorization method.
\n(i) 343
\n(ii) 729
\n(iii) 1331
\n(iv) 2744
\nSolution:
\n\"AP<\/p>\n

Question 2.
\nFind the cube root of the following numbers through estimation\u2019?
\n(i) 512
\n(ii) 2197
\n(iii) 3375
\n(iv) 5832
\nSolution:
\nStep 1: Start making groups of three digits starting from the unit place.
\ni.e, \\(\\overline{512}\\) First group is 512<\/p>\n

Step 2: First group i.e 512 will give us the units digit of the cube root. As 512 ends with 2, then its cube root ends with 8 (2 x 2 x 2) So the units place of the cube root will be 8.<\/p>\n

Step 3: Now take the second group i.e. 0. Which is 03<\/sup> < 1 < 23<\/sup>.
\nSo the least number is \u20180′.
\n\u2234 Tens digit of a cube root of a number be 0.
\n\u2234 \\(\\sqrt[3]{512}\\) = 08 = 8<\/p>\n

\"AP<\/p>\n

(ii) 2197
\nStep 1: Start making groups of three digits starting from the unit place.
\n\"AP<\/p>\n

Step 2: First group i.e., 197 will give us the units digit of the cube root.
\nAs 197 ends with 7, its cube root ends with 3. \u2018
\n[\u2235 3 x 3 x 3 = 27]
\n\u2234 Its units digit is 7.<\/p>\n

Step 3: Now take the second group i.e.,2
\nWe know that i3 < 2 < 2
\n\u2234 The least number be 1.
\n\u2234 The required number is 13.
\n\u2234 \\(\\sqrt[3]{2197}=\\sqrt[3]{13 \\times 13 \\times 13}=\\sqrt[\\not]]{(13)^{8}}\\)
\n= 13<\/p>\n

(iii) 3375
\nStep 1: Start making groups of three digits starting from the unit place.
\ni.e.;
\n\"AP<\/p>\n

Step 2: First group is 375. Its units digit is 5.
\n\u2234 The cube root is also ends with 5.
\n\u2234 The units place of the cube root will be 5.<\/p>\n

Step 3: Now take the second group,
\ni.e., 3 we know that 13<\/sup> < 33<\/sup> <23<\/sup>
\n\u2234 The least number is 1.
\n\u2234 The tens digit of a cube root will be 1.
\n\u2234 The required number = 15
\n\\(\\sqrt[3]{3375}=\\sqrt[3]{15 \\times 15 \\times 15}=\\sqrt[\\not]{15^{\\not 3}}=15\\)<\/p>\n

\"AP<\/p>\n

(iv) 5832
\nStep 1: Start making groups of three digits starting from the unit place.
\n\"AP<\/p>\n

Step 2: The units digit of 832 is 2.
\n\u2234 The cube root of the number ends with units digit 8.
\n[\u2235 8 x 8 x 8 = 512]<\/p>\n

Step 3: In the second group i.e., 5 lie between 1 and 6
\ni.e., 13<\/sup> < 5 < 23<\/sup>
\n\u2234 The tens digit of a number will bel.
\n\u2234 The required number is 18.
\n\u2234 \\(\\sqrt[3]{5832}=\\sqrt[3]{18 \\times 18 \\times 18}=\\sqrt[3]{(18)^{3}}\\)
\n= 18<\/p>\n

\"AP<\/p>\n

Question 3.
\nState true or false?
\n(i) Cube of an even number is an odd number
\n(ii) A perfect cube may end with two zeros
\n(iii) If a number ends with 5, then its cube ends with 5
\n(iv) Cube of a number ending with zero has three zeros at its right
\n(v) The cube of a single digit number may be a single digit number.
\n(vi) There is no perfect cube which ends with 8
\n(vii) The cube of a two digit number may be a three digit number.
\nSolution:
\n(i) Cube of an even number is an odd number (F)
\n(ii) A perfect cube may end with two zeros (F)
\n(iii) If a number ends with 5, then its cube ends with 5. (T)
\n(iv) Cube of a number ending with zero has three zeros at its right. (T)
\n(v) The cube of a single digit number may be a single digit number. (F)
\n(vi) There is no perfect cube which ends with 8(F)
\n(vii) The cube of a two digit number may be a three digit number. (F)<\/p>\n

\"AP<\/p>\n

Question 4.
\nFind the two digit number which is a square number and also a cubic number.
\nSolution:
\nThe two digited square and cubic
\nnumber is 64
\n\u2234 64 = 8 x 8 = 82<\/sup> \u21d2 \\(\\sqrt{64}\\) = 8
\n64 = 4 x 4 x 4 = 43<\/sup> \u21d2 \\(\\sqrt[3]{64}\\) = 4<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus AP Board 8th Class Maths Solutions Chapter 6 Square Roots and Cube Roots Ex 6.5 Textbook Questions and Answers. AP State Syllabus 8th Class Maths Solutions 6th Lesson Square Roots and Cube Roots Exercise 6.5 Question 1. Find the cube root of the following numbers by prime factorization method. (i) 343 (ii) … 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":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/6780"}],"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=6780"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/6780\/revisions"}],"predecessor-version":[{"id":40692,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/6780\/revisions\/40692"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/media?parent=6780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/categories?post=6780"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/tags?post=6780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}