[tex]a) \: \sqrt{ {15}^{2} + {20}^{2} } = \sqrt{225 + 400} = \sqrt{625} = 25[/tex]
[tex]b) \: \sqrt{ {30}^{2} - {18}^{2} } = \sqrt{900 - 324} = \sqrt{576} = 24[/tex]
[tex]c) \: \sqrt{ \frac{ {12}^{2} + {24}^{2} }{ {15}^{2} - {9}^{2} } } = \sqrt{ \frac{144 + 576}{225 - 81} } = \sqrt{ \frac{720}{144} } = \frac{12 \sqrt{5} }{12} = \sqrt{5} [/tex]
[tex]d) \: \sqrt{ \frac{ {5}^{2} + {12}^{2} }{ {25}^{2} - {15}^{2} } } = \sqrt{ \frac{25 + 144}{625 - 225} } = \sqrt{ \frac{169}{400} } = \frac{13}{20} [/tex]
