(i) 12 and 13

(ii) 25 and 26

(iii) 99 and 100.

Answer :

We know that numbers between \(n^2\) and \((n + 1)^2\) = 2n

(i) Numbers between \(12^2\) and \(13^2\) = (2n) = \(2 \times 12\) = 24

(ii) Numbers between \(25^2\) and \(26^2\) = \(2 \times 25\) = 50 [ n = 25]

(iii) Numbers between \(99^2\) and \(100^2\) = \(2 \times 99\) = 198 [ n = 99]

- 1.What will be the unit digit of the squares of the following numbers? (i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234 (vi) 20387 (vii) 52698 (viii) 99880 (ix) 12796 (x) 55555
- 2. The following numbers are not perfect squares. Give reason. (i) 1057 (ii) 23453 (iii) 7928 (iv) 222222 (v) 64000 (vi) 89722 (vii) 222000 (viii) 505050
- 3.The squares of which of the following would be odd numbers? (i) 431 (ii) 2826 (iii) 7779 (iv) 82004
- 4.Observe the following pattern and find the missing digits. \(11^2\) = 121 \(101^2\) = 10201 \(1001^2\) = 1002001 \(100001^2\) = 1…2…1 \(10000001^2\) = ………
- 5.Observe the following pattern and supply the missing numbers. \(11^2\) = 121 \(101^2\) = 10201 \(10101^2\) = 102030201 \(1010101^2\) = ………. \(……….^2\) = 10203040504030201
- 6.Using the given pattern, find the missing numbers. \(1^2 + 2^2 + 2^2 = 3^2\) \(2^2 + 3^2 + 6^2 = 7^2\) \(3^2 + 4^2 + 12^2 = 13^2\) \(4^2 + 5^2 + ….^2 = 21^2\) \(5^2 + ….^2 + 30^2 = 31^2\) \(6^2 + 7^2 + …..^2 = ……2\)
- 7.Without adding, find the sum. (i) 1 + 3 + 5 + 7 + 9 (ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 (iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
- 8. (i) Express 49 as the sum of 7 odd numbers. (ii) Express 121 as the sum of 11 odd numbers.

- NCERT solutions for class 8 maths chapter 1 Rational Numbers
- NCERT solutions for class 8 maths chapter 2 Linear Equations in One Variable
- NCERT solutions for class 8 maths chapter 3 Understanding Quadrilaterals
- NCERT solutions for class 8 maths chapter 4 Practical Geometry
- NCERT solutions for class 8 maths chapter 5 Data Handling
- NCERT solutions for class 8 maths chapter 6 Squares and Square Roots
- NCERT solutions for class 8 maths chapter 7 Cube and Cube Roots
- NCERT solutions for class 8 maths chapter 8 Comparing Quantities
- NCERT solutions for class 8 maths chapter 9 Algebraic Expressions and Identities
- NCERT solutions for class 8 maths chapter 10 Visualising Solid Shapes
- NCERT solutions for class 8 maths chapter 11 Mensuration
- NCERT solutions for class 8 maths chapter 12 Exponents and Powers
- NCERT solutions for class 8 maths chapter 13 Direct and Inverse Proportions
- NCERT solutions for class 8 maths chapter 14 Factorization
- NCERT solutions for class 8 maths chapter 15 Introduction to Graphs
- NCERT solutions for class 8 maths chapter 16 Playing with Numbers

- NCERT solutions for class 8 science chapter 1 Crop Production & Management
- NCERT solutions for class 8 science chapter 2 Microorganisms: Friend and Foe
- NCERT solutions for class 8 science chapter 3 Synthetic Fibers and Plastics
- NCERT solutions for class 8 science chapter 4 Materials: Metals and Nonmetals
- NCERT solutions for class 8 science chapter 5 Coal and Petroleum
- NCERT solutions for class 8 science chapter 6 Combustion and Flame
- NCERT solutions for class 8 science chapter 7 Conservation of Plants and Animals
- NCERT solutions for class 8 science chapter 8 Cell-Structure and Function
- NCERT solutions for class 8 science chapter 9 Reproduction in Animals
- NCERT solutions for class 8 science chapter 10 Reaching the Age of Adolsence
- NCERT solutions for class 8 science chapter 11 Force and Pressure
- NCERT solutions for class 8 science chapter 12 Friction
- NCERT solutions for class 8 science chapter 13 sound
- NCERT solutions for class 8 science chapter 14 Chemical Effects of Electric Current
- NCERT solutions for class 8 science chapter 15 Some Natural Phenomena
- NCERT solutions for class 8 science chapter 16 Light
- NCERT solutions for class 8 science chapter 17 Stars and the Solar System
- NCERT solutions for class 8 science chapter 18 Pollution of Air and Water