Question
Evaluate:
$\sqrt{4\frac{73}{324}}$
$\sqrt{4\frac{73}{324}}$
✓
Answer
$\sqrt{4\frac{73}{324}}$
$=\sqrt{\frac{4\times324+73}{324}}$
$=\sqrt{\frac{1296+73}{324}}$
$=\sqrt{\frac{1369}{324}}$
$\begin{array}{c|c}37&1369\\\hline37&37\\\hline&1\end{array}$
$\begin{array}{c|c}2&324\\\hline2&162\\\hline3&81\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$=\sqrt{\frac{37\times37}{2\times2\times3\times3\times3\times3}}$
$=\frac{37}{2\times3\times3}$
$=\frac{37}{18}$
$=2\frac{1}{18}$
$=\sqrt{\frac{4\times324+73}{324}}$
$=\sqrt{\frac{1296+73}{324}}$
$=\sqrt{\frac{1369}{324}}$
$\begin{array}{c|c}37&1369\\\hline37&37\\\hline&1\end{array}$
$\begin{array}{c|c}2&324\\\hline2&162\\\hline3&81\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$=\sqrt{\frac{37\times37}{2\times2\times3\times3\times3\times3}}$
$=\frac{37}{2\times3\times3}$
$=\frac{37}{18}$
$=2\frac{1}{18}$
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