The DAV Class 8 Maths Book Solutions and DAV Class 8 Maths Chapter 1 Worksheet 2 Solutions of Squares and Square Roots offer comprehensive answers to textbook questions.
DAV Class 8 Maths Ch 1 WS 2 Solutions
Find the square root of the following numbers by the repeated subtraction method.
Question 1.
16
Solution:
\(\sqrt{16}\)
(i) 16 – 1 = 15
(ii) 15 – 3 = 12
(iii) 12 – 5 = 7
(iv) 7 – 7 = 0
We have subtracted the successive odd numbers from 16 and obtained 0 in the forth step.
∴ \(\sqrt{16}\) = 4
Question 2.
49
Solution:
\(\sqrt{49}\)
(i) 49 – 1 = 48
(ii) 48 – 3 = 45
(iii) 45 – 5 = 40
(iv) 40 – 7 = 33
(v) 33 – 9 = 24
(vi) 24 – 11 = 13
(vii) 13 – 13 = 0
We have subtracted the successive odd numbers from 49 and obtained 0 in the seventh step.
∴ \(\sqrt{49}\) = 7
Question 3.
64
Solution:
\(\sqrt{64}\)
(i) 64 – 1 = 63
(ii) 63 – 3 = 60
(iii) 60 – 5 = 55
(iv) 55 – 7 = 48
(v) 48 – 9 = 39
(vi) 39 – 11 = 28
(vii) 28 – 13 = 15
(viii) 15 – 15 = 0
We have subtracted the successive odd numbers from 64 and obtained 0 in the eighth step.
∴ \(\sqrt{64}\) = 8
Question 4.
100
Solution.
\(\sqrt{100}\)
(i) 100 – 1 = 99
(ii) 99 – 3 = 96
(iii) 96 – 5 = 91
(iv) 91 – 7 = 84
GO 84 – 9 = 75
(vi) 75 – 11 = 64
(vii) 64 – 13 = 51
(viii) 51 – 15 = 36
(ix) 36 – 17 = 19
(x) 19 – 19 = 0
We have subtracted the successive odd numbers from 100 and obtained 0 in the tenth step.
∴ \(\sqrt{100}\) = 10
Question 5.
169
Solution:
\(\sqrt{169}\)
CD 169 – 1 = 168
(ii) 168 – 3 = 165
(iii) 165 – 5 = 160
(iv) 160 – 7 = 153
(v) 153 – 9 = 144
(vi) 144 – 11 = 133
(vii) 133 – 13 = 120
(viii) 120 – 15 = 105
(ix) 105 – 17 = 88
(x) 88 – 19 = 69
(xi) 69 – 21 = 48
(xii) 48 – 23 = 25
(xiii) 25 – 25 = 0
We have subtracted successive odd numbers from 169 and obtained 0 in the thirteenth step.
∴ \(\sqrt{169}\) = 13
Question 6.
81
Solution:
\(\sqrt{81}\)
(i) 81 – 1 = 80
(ii) 80 – 3 = 77
(iii) 77-5 = 72
(iv) 72 – 7 = 65
(v) 65 – 9 = 56
(vi) 56 – 11 = 45
(vii) 45 – 13 = 32
(viii) 32 – 15 = 17
(ix) 17 – 17 = 0
We have subtracted successive odd natural numbers from 81 and obtained 0 in the ninth step.
∴ \(\sqrt{81}\) = 9.
Question 7.
256
Solution:
\(\sqrt{256}\)
(i) 256 – 1 = 255
(ii) 255 – 3 = 252
(iii) 252 – 5 = 247
(iv) 247 – 7 = 240
(v) 240 – 9 = 231
(vi) 231 – 11 = 220
(vii) 220 – 13 = 207
(viii) 207 – 15 = 192
(ix) 192 – 17 = 175
(x) 175 – 19 = 156
(xi) 156 – 13 = 135
(xii) 135 – 15 = 112
(xiii) 112 – 25 = 87
(xiv) 87 – 27 = 60
(xv) 60 – 29 = 31
(xvi) 31 – 31 = 0
We have subtracted successive odd natural numbers from 256 and obtained 0 in the sixteenth step.
∴ \(\sqrt{256}\) = 16.
Question 8.
144
Solution:
\(\sqrt{144}\)
1. 144 – 1 = 143
2. 143 – 3 = 140
3. 140 – 5 = 135
4. 135 – 7 = 128
5. 128 – 9 = 119
6. 119 – 11 = 108
7. 108 – 13 = 95
8. 95 – 15 = 80
9. 80 – 17 = 63
10. 63 – 19 = 44
11. 44 – 21 = 23
12. 23 – 23 = 0
We have subtracted successive odd natural numbers from 144 and obtained 0 in the twelfth step.
∴ \(\sqrt{144}\) = 12.
DAV Class 8 Maths Chapter 1 Worksheet 2 Notes
- The square root of an odd number is odd.
- The square root of an even number is even.
- The symbol of square root is √ or raised to the power
- If m is a square root of n, then n is the square of m.
Methods to find the Square Roots:
(i) Repeated Subtraction Method
Example 1.
Find \(\sqrt{49}\) by repeated subtraction method.
Solution:
(i) 49 – 1 = 48
(ii) 48 – 3 = 45
(iii)45 – 5 = 40
(iv) 40 – 7 = 33
(u) 33 – 9 = 24
(vi) 24 – 11 = 13
(vii) 13 – 13 = 0
We have subtracted the successive odd number 1,3, 5, 7, 9, 11 and 13 and got 0 in the seventh step.
∴ \(\sqrt{49}\) = 7.
Example 2.
Find the square root of 81 by repeated subtraction method.
Solution:
(i) 81 – 1 = 80
(ii) 80 – 3 = 77
(iii) 77 – 5 = 72
(iv) 72 – 7 = 65
(v) 65 – 9 = 56
(vi) 56 – 11 = 45
(vii) 45 – 13 = 32
(viii) 32 – 15 = 17
(ix) 17 – 17 = 0
We have subtracted the successive odd number and obtained 0 in the ninth step.
∴ \(\sqrt{81}\) = 9.