[tex]a) \sqrt{144 + 81} = \sqrt{225} = 15 \\ b) \sqrt{225 + 81 + 256} = \sqrt{400} = 20 \\ c) \sqrt{225 + 400} = \sqrt{625 } = 25 \\ d) \sqrt{(30 - 24)(30 + 24)} = \sqrt{6 \times 54} = \sqrt{324} = 18 \\ e) \sqrt{ {15}^{2} + 64} = \sqrt{225 + 64} = \sqrt{289} = 17[/tex]
[tex]f) \sqrt{( {13}^{2} - {5}^{2} ) \times {3}^{4} } = \sqrt{((13 - 5)(13 + 5)) \times {3}^{4} } = \sqrt{(8 \times 18) \times {3}^{4} } = \sqrt{144 - \times {3}^{4} } = 12 \times {3}^{2} = 108 \\ g) \sqrt{ {2}^{6} \times {7}^{2} + {(2 \times 3 \times 7)}^{2} } = \sqrt{ {2}^{6} \times {7}^{2} + {42}^{2} } = \sqrt{ {2}^{6} \times {7}^{2} + {(6 \times 7)}^{2} } = \sqrt{ {2}^{6} \times {7}^{2} + {6}^{2} \times {7}^{2} } = \sqrt{100 \times {7}^{2} } = 10 \times 7 = 70[/tex]
