Evaluate: 625 729 - Vidyadip

Question

Evaluate: $\sqrt{\frac{625}{729}}$

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Answer

$\sqrt{\frac{625}{729}}$ $\begin{array}{c|c}5&625\\\hline5&125\\\hline5&25\\\hline5&5\\\hline&1\end{array}$ $\begin{array}{c|c}3&729\\\hline3&243\\\hline3&81\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$ $=\sqrt{\frac{\overline{5\times5}\times\overline{5\times5}}{\overline{3\times3}\times\overline{3\times3}\times\overline{3\times3}}}$ $=\frac{5\times5}{3\times3\times3}$ $=\frac{25}{27}$

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