Question

Find the square root by long division method.
(i)17956 (ii) 11025 (iii) 6889 (iv) 1764
(v) 418609​

Answer 1

$\begin{array}{r|lllll}&1&3&4&&\\\cline{2-6}1&1&7&9&5&6\\&1&&&&\\\cline{2-6}23&&7&9&&\\&&6&9&&\\\cline{2-6}264&&1&0&5&6\\&&1&0&5&6\\\cline{2-6}&&&&&0\\\cline{2-6}\end{array}$

$\begin{array}{r|lllll}&1&0&5&&\\\cline{2-6}1&1&1&0&2&5\\&1&&&&\\\cline{2-6}205&&1&0&2&5\\&&1&0&2&5\\\cline{2-6}&&&&&0\\\cline{2-6}\end{array}$

$\begin{array}{r|llll}&8&3&&\\\cline{2-5}8&6&8&8&9\\&6&4&&\\\cline{2-5}164&&4&8&9\\&&4&8&9\\\cline{2-5}&&&&0\\\cline{2-5}\end{array}$

$\begin{array}{r|llll}&4&2&&\\\cline{2-5}4&1&7&6&4\\&1&6&&\\\cline{2-5}82&&1&6&4\\&&1&6&4\\\cline{2-5}&&&&0\\\cline{2-5}\end{array}$

$\begin{array}{r|llllll}&6&4&7&&&\\\cline{2-7}6&4&1&8&6&0&9\\&3&6&&&&\\\cline{2-7}124&&5&8&6&&\\&&4&9&6&&\\\cline{2-7}1287&&&9&0&0&9\\&&&9&0&0&9\\\cline{2-7}&&&&&&0\\\cline{2-7}\end{array}$

$\textbf{Thus, we have}$

$\text{(i)}\bf\sqrt{17956}=134$

$\text{(ii)}\bf\sqrt{11025}=105$

$\text{(iii)}\bf\sqrt{6889}=83$

$\text{(iv)}\bf\sqrt{1764}=42$

$\text{(v)}\bf\sqrt{418609}=647$

Answer 2

Answer:

i)17956=134

i)17956=134\text{(ii)}\bf\sqrt{11025}=105(ii)11025=105

i)17956=134\text{(ii)}\bf\sqrt{11025}=105(ii)11025=105\text{(iii)}\bf\sqrt{6889}=83(iii)6889=83

i)17956=134\text{(ii)}\bf\sqrt{11025}=105(ii)11025=105\text{(iii)}\bf\sqrt{6889}=83(iii)6889=83\text{(iv)}\bf\sqrt{1764}=42(iv)1764=42

i)17956=134\text{(ii)}\bf\sqrt{11025}=105(ii)11025=105\text{(iii)}\bf\sqrt{6889}=83(iii)6889=83\text{(iv)}\bf\sqrt{1764}=42(iv)1764=42\text{(v)}\bf\sqrt{418609}=647(v)418609=647