DAV Class 8 Maths Chapter 1 Worksheet 2
Squares and Square Roots Worksheet 2
Find the square root of the following numbers by the repeated subtraction method
(a) 16
\[ \begin{align*} 16 - 1 &= 15 \\ 15 - 3 &= 12 \\ 12 - 5 &= 7 \\ 7 - 7 &= 0 \\ \sqrt{16} &= 4 \end{align*} \]
Answer \( \color{red}\sqrt{16} = 4 \)
(b) 49
\[ \begin{align*} 49 - 1 &= 48 \\ 48 - 3 &= 45 \\ 45 - 5 &= 40 \\ 40 - 7 &= 33 \\ 33 - 9 &= 24 \\ 24 - 11 &= 13 \\ 13 - 13 &= 0 \\ \sqrt{49} &= 7 \end{align*} \]
Answer \( \color{red}\sqrt{49} = 7 \)
(c) 64
\[ \begin{align*} 64 - 1 &= 63 \\ 63 - 3 &= 60 \\ 60 - 5 &= 55 \\ 55 - 7 &= 48 \\ 48 - 9 &= 39 \\ 39 - 11 &= 28 \\ 28 - 13 &= 15 \\ 15 - 15 &= 0 \\ \sqrt{64} &= 8 \end{align*} \]
Answer \( \color{red}\sqrt{64} = 8 \)
(d) 100
\[ \begin{align*} 100 - 1 &= 99 \\ 99 - 3 &= 96 \\ 96 - 5 &= 91 \\ 91 - 7 &= 84 \\ 84 - 9 &= 75 \\ 75 - 11 &= 64 \\ 64 - 13 &= 51 \\ 51 - 15 &= 36 \\ 36 - 17 &= 19 \\ 19 - 19 &= 0 \\ \sqrt{100} &= 10 \end{align*} \]
Answer \( \color{red}\sqrt{100} = 10 \)
(e) 169
\[ \begin{align*} 169 - 1 &= 168 \\ 168 - 3 &= 165 \\ 165 - 5 &= 160 \\ 160 - 7 &= 153 \\ 153 - 9 &= 144 \\ 144 - 11 &= 133 \\ 133 - 13 &= 120 \\ 120 - 15 &= 105 \\ 105 - 17 &= 88 \\ 88 - 19 &= 69 \\ 69 - 21 &= 48 \\ 48 - 23 &= 25 \\ 25 - 25 &= 0 \\ \sqrt{169} &= 13 \end{align*} \]
Answer \( \color{red}\sqrt{169} = 13 \)
(f) 81
\[ \begin{align*} 81 - 1 &= 80 \\ 80 - 3 &= 77 \\ 77 - 5 &= 72 \\ 72 - 7 &= 65 \\ 65 - 9 &= 56 \\ 56 - 11 &= 45 \\ 45 - 13 &= 32 \\ 32 - 15 &= 17 \\ 17 - 17 &= 0 \\ \sqrt{81} &= 9 \end{align*} \]
Answer \( \color{red}\sqrt{81} = 9 \)
(g) 256
\[ \begin{align*} 256 - 1 &= 255 \\ 255 - 3 &= 252 \\ 252 - 5 &= 247 \\ 247 - 7 &= 240 \\ 240 - 9 &= 231 \\ 231 - 11 &= 220 \\ 220 - 13 &= 207 \\ 207 - 15 &= 192 \\ 192 - 17 &= 175 \\ 175 - 19 &= 156 \\ 156 - 21 &= 135 \\ 135 - 23 &= 112 \\ 112 - 25 &= 87 \\ 87 - 27 &= 60 \\ 60 - 29 &= 31 \\ 31 - 31 &= 0 \\ \sqrt{256} &= 16 \end{align*} \]
Answer \( \color{red}\sqrt{256} = 16 \)
(h) 144
\[ \begin{align*} 144 - 1 &= 143 \\ 143 - 3 &= 140 \\ 140 - 5 &= 135 \\ 135 - 7 &= 128 \\ 128 - 9 &= 119 \\ 119 - 11 &= 108 \\ 108 - 13 &= 95 \\ 95 - 15 &= 80 \\ 80 - 17 &= 63 \\ 63 - 19 &= 44 \\ 44 - 21 &= 23 \\ 23 - 23 &= 0 \\ \sqrt{144} &= 12 \end{align*} \]
Answer \( \color{red}\sqrt{144} = 12 \)