Question

Find the square root of 15129 by division method

Answer 1

`\underline{\ \ \ \ \ \ 123}\\1\ \ \ |15129\\\underline1\\22\ |\ 51\\\underline\ \ \ \ \\243|\ \ 729\\\underline\ \ \ \ \ \\.\qquad\ \ \ 0`

`√(15129)=123`

`\begin{array}c15129&3\\5043&3\\1681&41\\41&41\\1\end{array}15129=3\cdot3\cdot41\cdot41=3^2\cdot41^2\\\\√(15129)=√(3^2\cdot41^2)=\sqrt3^2}\cdot√(41^2)=3\cdot41=123`

`Used:\\\\√(a\cdot b)=√(a)\cdot√(b)\\\\√(a^2)=a\ for\ a\geq0`