We have,
\(\frac{\sqrt{48}}{\sqrt{243}}=\sqrt{\frac{48}{243}}{}\)
= \(\sqrt{\frac{2\times2\times2\times2\times3}{3\times3\times3\times3\times3}}\)
= \(\frac{\sqrt{2\times2\times2\times2}}{\sqrt{3\times3\times3\times3}}\)
= \(\frac{2\times2}{3\times3}\)
= \(\frac{4}{9}\)
