[tex] \sqrt{18 \times 32} = \sqrt{2 \times {3}^{2} \times 2 \times 4 {}^{2} } = \sqrt{2 {}^{2} \times 3 {}^{2} \times {4}^{2} } = 2 \times 3 \times 4 = 24[/tex]

[tex] \sqrt{8 \times 98} = \sqrt{2 {}^{2} \times 2 \times {7}^{2} \times 2} = \sqrt{ {2}^{2} \times 2 {}^{2} \times {7}^{2} } = 2 \times 2 \times 7 = 28[/tex]

[tex] \sqrt{3.6 \times 14.4} = \sqrt{ \frac{36}{10} \times \frac{144}{10} } = \sqrt{ \frac{ {6}^{2} \times {12}^{2} }{ {10}^{2} } } = \frac{6 \times 12}{10} = \frac{72}{10} = \frac{36}{5} = 7.2[/tex]

[tex] \sqrt{75 \times 48} = \sqrt{3 \times {5}^{2} \times 3 \times {4}^{2} } = \sqrt{ {3}^{2} \times {4}^{2} \times {5}^{2} } = 3 \times 4 \times 5 = 60[/tex]

[tex] \sqrt{288 \times 50} = \sqrt{2 \times {12}^{2} \times 2 \times {5}^{2} } = \sqrt{ {2}^{2} \times {5}^{2} \times {12}^{2} } = 2 \times 5 \times 12 = 120[/tex]

[tex] \sqrt{4.5 \times 72} = \sqrt{4.5 \times 2 \times {6}^{2} } = \sqrt{9 \times {6}^{2} } = \sqrt{ {3}^{2} \times {6}^{2} } = 3 \times 6 = 18[/tex]