finding square root I want to know how to find the square root/cube root of a number ending with zero.
For instance, $\sqrt{1024}$ : though it's a perfect square, there is a shortcut. Like wise how can I find the $\sqrt{2240}$ or any number ending with zero?
Thanks in advance!


By $$(10a+b)^2 = a\times 100a+(10\times 2a+b)\times b$$

We can use long division,
\begin{array}{rrrr}
     &         &  3   & 2 \\
     &         & --  & -- \\
   3 & \sqrt{} & 10  & 24 \\
     &         &  9  &    \\
     &         & --  & -- \\
     &         &  1  & 24 \\
  62 &         &  1  & 24 \\
     &         & --  & -- \\
     &         &     &  0 \\
\end{array}
which means $32^2=(10\times 3+2)^2=100\times 9+62 \times 2=1024$,
thus $\sqrt{1024}=32$.

By $$(10a+b)^3 = a^2\times 1000a+(100\times 3a^2+10\times 3ab+b^2)\times b$$

We can use long division,
\begin{array}{rrr}
       &            &  2   &  3 \\
       &            & --  &  -- \\
     4 & \sqrt[3]{} & 12  & 167 \\
       &            &  8  &     \\
       &            & --  &  -- \\
       &            &  4  & 167 \\
  1389 &            &  4  & 167 \\
       &            & --  &  -- \\
       &            &     &   0 \\
\end{array}
where $4=\color{red}{2}^2$ and 
$1389=100\times 3\times \color{red}{2}^2+10\times 3\times \color{red}{2} \times \color{blue}{3}+\color{blue}{3}^2$
therefore $\sqrt[3]{12167}=23$.
