Answer :

Using the method of repeated subtraction of consecutive odd numbers, we have

(i) 100 – 1 = 99, 99 – 3 = 96, 96 – 5 = 91, 91 – 7 = 84, 84 – 9 = 75, 75 – 11 = 64, 64 – 13 = 51, 51 – 15 = 36, 36 – 17 = 19, 19 – 19 = 0

Thus it takes 10 times repetition to reach 0.

So, \(\sqrt{100} = 10\)

(ii) 169 – 1 = 168, 168 – 3 = 165, 165 – 5 = 160, 160 – 7 = 153, 153 – 9 = 144, 144 – 11 = 133, 133 – 13 = 120, 120 – 15 = 105, 105 – 17 = 88, 88 – 19 = 69, 69 – 21 = 48, 48 – 23 = 25, 25 – 25 = 0

It takes thirteen times repetition to reach 0.

Hence, \(\sqrt{169} = 13\)

- 1.What could be the possible ‘one’s’ digits of the square root of each of the following numbers? (i) 9801 (ii) 99856 (iii) 998001 (iv) 657666025
- 2.Without doing any calculation, find the numbers which are surely not perfect squares. (i) 153 (ii) 257 (iii) 408 (iv) 441
- 4.Find the square roots of the following numbers by the prime factorisation Method. (i) 729 (ii) 400 (iii) 1764 (iv) 4096 (v) 7744 (vi) 9604 (vii) 5929 (viii) 9216 (ix) 529 (x) 8100
- 5.For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained. (i) 252 (ii) 180 (iii) 1008 (iv) 2028 (v) 1458 (vi) 768
- 6.For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained. (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620
- 7.The students of class VIII of a school donated ₹ 2401 in all, for the Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.
- 8.2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
- 9.Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.
- 10.Find the smallest number that is divisible by each of the numbers 8, 15 and 20.

- 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