{"id":27257,"date":"2021-06-30T09:50:35","date_gmt":"2021-06-30T04:20:35","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=27257"},"modified":"2022-03-02T10:31:33","modified_gmt":"2022-03-02T05:01:33","slug":"ncert-solutions-for-class-8-maths-chapter-6-ex-6-1","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-6-ex-6-1\/","title":{"rendered":"NCERT Solutions for Class 8 Maths Chapter 6 Square and Square Roots Ex 6.1"},"content":{"rendered":"

These NCERT Solutions for Class 8 Maths<\/a> Chapter 6 Square and Square Roots Ex 6.1 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 8 Maths Chapter 6 Square and Square Roots Exercise 6.1<\/h2>\n

Question 1.
\nWhat will be the unit digit of the squares of the following numbers?
\n(i) 81
\n(ii) 272
\n(iii) 799
\n(iv) 3853
\n(v) 1234
\n(vi) 26387
\n(vii) 52698
\n(viii) 99880
\n(ix) 12796
\n(x) 55555
\nSolution:
\n(i) The unit digit of (81)2<\/sup> is 1 (1 \u00d7 1 = 1)
\n(ii) The unit digit of (272)2<\/sup> is 4 (2 \u00d7 2 = 4)
\n(iii) The unit digit of (799)2<\/sup> is 1 (9 \u00d7 9 = 81)
\n(iv) The unit digit of (3853)2<\/sup> is 9 (3 \u00d7 3 = 9)
\n(v) The unit digit of (1234)2<\/sup> is 6 (4 \u00d7 4 = 16)
\n(vi) The unit digit of (26387)2<\/sup> is 9 (7 \u00d7 7 = 49)
\n(vii) The unit digit of (52698)2<\/sup> is 4 (8 \u00d7 8 = 64)
\n(viii) The unit digit of (99880)2<\/sup> is 0 (0 \u00d7 0 = 0)
\n(ix) The unit digit of (12796)2<\/sup> is 6 (6 \u00d7 6 = 36)
\n(x) The unit digit of (55555)2<\/sup> is 5 (5 \u00d7 5 = 25)<\/p>\n

\"NCERT<\/p>\n

Question 2.
\nThe following numbers are obviously not perfect squares. Give reason.
\n(i) 1057
\n(ii) 23453
\n(iii) 7928
\n(iv) 222222
\n(v) 64000
\n(vi) 89722
\n(vii) 222000
\n(viii) 505050
\nSolution:
\n(i) 1057 is not a perfect square,
\nAs the last digit is 7 [It is not one of 0, 1, 4, 5, 6, and 9].<\/p>\n

(ii) 23453 is not a perfect square,
\nAs the last digit is 3 [It is not one of 0, 1, 4, 5, 6, and 9].<\/p>\n

(iii) 7928 is not a perfect square,
\nAs the last digit is 8 [It is not one of 0, 1, 4, 5, 6, and 9].<\/p>\n

(iv) 222222 is not a perfect square,
\nAs the last digit is 2 [It is not one of 0, 1, 4, 5, 6, and 9].<\/p>\n

(v) 64000 is not a perfect square,
\nAs the number of zeros is odd.<\/p>\n

(vi) 89722 is not a perfect square,
\nAs the last digit is 2 [It is not one of 0, 1, 4, 5, 6, and 9].<\/p>\n

(vii) 222000 is not a perfect square,
\nAs the number of zeros is odd.<\/p>\n

(viii) 505050 is not a perfect square,
\nAs the number of zeros is odd.<\/p>\n

Question 3.
\nThe squares of which of the following would be odd numbers?
\n(i) 431
\n(ii) 2826
\n(iii) 7779
\n(iv) 82004
\nNote: The square of an odd natural number is always odd and that of an even number always an even number.
\nSolution:
\n(i) The square of 431 is an odd number.
\n(ii) The square of2826 is an even number.
\n(iii) The square of 7779 is an odd number.
\n(iv) The square of82004 is an even number.<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nObserve the following pattern and find the missing digits.
\n112<\/sup> = 121
\n1012<\/sup> = 10201
\n10012<\/sup> = 1002001
\n1000012<\/sup> = 1………2……..1
\n100000012<\/sup> = …………….
\nSolution:
\nBy observing the above pattern, we get
\n(i) 1000012<\/sup> = 10000200001
\n(ii) 100000012<\/sup> = 100000020000001<\/p>\n

Question 5.
\nObserve the following pattern and supply the missing number.
\n(a) 112<\/sup> = 121
\n1012<\/sup> = 10201
\n101012<\/sup> = 102030201
\n10101012<\/sup> = …………….
\n………..2<\/sup> = 1020304030201
\nSolution:
\nBy observing the above pattern, we get
\n(I) (1010101)2<\/sup> = 1020304030201
\n(ii) 10203040504030201 = (101010101)2<\/sup><\/p>\n

\"NCERT<\/p>\n

Question 6.
\nUsing the given pattern. Find the missing numbers.
\n12<\/sup> + 22<\/sup> + 22<\/sup> = 32<\/sup>
\n22<\/sup> + 32<\/sup> + 62<\/sup> = 72<\/sup>
\n32<\/sup> + 42<\/sup> + 122<\/sup> = 132<\/sup>
\n42<\/sup> + 52<\/sup> + ……2<\/sup> = 212<\/sup>
\n52<\/sup> + …..2<\/sup> + 302<\/sup> = 312<\/sup>
\n62<\/sup> + 72<\/sup> + ……2<\/sup> = ……..2<\/sup>
\nSolution:
\n42<\/sup> + 52<\/sup> + 202<\/sup> = 212<\/sup>
\n52<\/sup> + 62<\/sup> + 302<\/sup> = 312<\/sup>
\n62<\/sup> + 72<\/sup> + 422<\/sup> = 432<\/sup>
\nNote: To find pattern
\nThe third number is related to the first and second numbers. How?
\nThe fourth number is related to the third number. How?<\/p>\n

Question 7.
\nWithout adding, find the sum
\n(i) 1 + 3 + 5 + 7 + 9
\n(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
\n(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
\nSolution:
\n(i) Sum of the first 5 odd numbers = 52<\/sup> = 25
\n(ii) Sum of the first 10 odd numbers = 102<\/sup> = 100
\n(iii) Sum of the first 12 odd numbers = 122<\/sup> = 144<\/p>\n

\"NCERT<\/p>\n

Question 8.
\n(i) Express 49 as the sum of 7 odd numbers.
\n(ii) Express 121 as to the sum of 11 odd numbers.
\nSolution:
\n(i) 72<\/sup> = 49
\n1 + 3 + 5 + 7 + 9 + 11 + 13 (First 7 odd numbers)
\n(ii) 112<\/sup> = 121
\n1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 (First 11 odd numbers)<\/p>\n

Question 9.
\nHow many numbers lie between squares of the following numbers?
\n(i) 12 and 13
\n(ii) 25 and 26
\n(iii) 99 and 100
\nSolution:
\nNote: Since between n and (n + 1) there are 2n non-square numbers
\n(i) Between 122<\/sup> and 132<\/sup>, there are 2 \u00d7 12 numbers i.e. 24 numbers
\n(ii) Between 252<\/sup> and 262<\/sup>, there are 2 \u00d7 25 numbers i.e. 50 numbers
\n(iii) Between 992<\/sup> and 1002<\/sup>, there are 2 \u00d7 99 numbers i.e. 198 numbers
\nNote: For any number ending with 5, the square is a (a + 1) \u00d7 100 + 25
\n(i) 352<\/sup>
\n= 3(3 + 1) \u00d7 100 + 25
\n= 1200 + 25
\n= 1225<\/p>\n

\"NCERT<\/p>\n

(ii) 552<\/sup>
\n= 5(5 + 1) \u00d7 100 + 25
\n= 3000 + 25
\n= 3025<\/p>\n

(iii) 1252<\/sup>
\n= 12(12 + 1) \u00d7 100 + 25
\n= 12 \u00d7 13 \u00d7 100 + 25
\n= 15600 + 25
\n= 15625<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 8 Maths Chapter 6 Square and Square Roots Ex 6.1 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 8 Maths Chapter 6 Square and Square Roots Exercise 6.1 Question 1. What will be the unit digit of the squares of the following numbers? …<\/p>\n

NCERT Solutions for Class 8 Maths Chapter 6 Square and Square Roots Ex 6.1<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[7],"tags":[],"yoast_head":"\nNCERT Solutions for Class 8 Maths Chapter 6 Square and Square Roots Ex 6.1 - MCQ Questions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-6-ex-6-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 8 Maths Chapter 6 Square and Square Roots Ex 6.1 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 8 Maths Chapter 6 Square and Square Roots Ex 6.1 Questions and Answers are prepared by our highly skilled subject experts. 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