Answer: 5/16
Step-by-step explanation:
For this question, note that:
[tex]\sqrt{16}=4\\ \\ \sqrt{25}=5 \\\\\sqrt{81}=9\\\\\sqrt{144}=12\\\\\sqrt{225}=15\\\\\sqrt{729}=27[/tex]
This means we can rewrite the given expression as:
[tex]\left(\frac{15}{27}-\frac{5}{12} \right) \div \frac{4}{9}\\\\=\left(\frac{5}{9}-\frac{5}{12} \right) \div \frac{4}{9}\\\\=\left(\frac{(5)(12)-(5)(9)}{(9)(12)} \right) \div \frac{4}{9}\\\\=\frac{15}{108} \div \frac{4}{9}\\\\=\frac{5}{36} \div \frac{4}{9}\\\\=\frac{5}{36} \times \frac{9}{4}\\\\=\frac{45}{144}\\\\=\boxed{\frac{5}{16}}[/tex]
