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[tex] \sqrt{432} = \sqrt{3 \times 3 \times 3 \times 2 \times 2 \times 2 \times 2} = \sqrt{3 \times 9 \times 4 \times 4} = \sqrt{3 \times 9 \times 16} = \sqrt{3 \times 144} = 12 \sqrt{3} [/tex]
[tex] \sqrt{448} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7} = \sqrt{4 \times 4 \times 4 \times 7} = \sqrt{16 \times 4 \times 7} = \sqrt{64 \times 7} = 8 \sqrt{7} [/tex]
[tex] \sqrt{864} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3} = \sqrt{4 \times 4 \times 2 \times 9 \times 3} = \sqrt{16 \times 9 \times 6} = \sqrt{144 \times 6} = 12 \sqrt{6} [/tex]
[tex] \sqrt{972} = \sqrt{2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3} = \sqrt{4 \times 9 \times 9 \times 3} = \sqrt{4 \times 81 \times 3} = \sqrt{324 \times 3} = 18 \sqrt{3} [/tex]
[tex] \sqrt[3]{432} = \sqrt[3]{2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3} = \sqrt[3]{4 \times 2 \times 2 \times 9 \times 3} = \sqrt{8 \times 2 \times 9 \times 3} = \sqrt{8 \times 27 \times 2} = \sqrt{216 \times 2} = 6 \sqrt{2} [/tex]
[tex] \sqrt[3]{1375} = \sqrt[3]{5 \times 5 \times 5 \times 11} = \sqrt[3]{125 \times 11} = 5 \sqrt[3]{11} [/tex]
[tex] \sqrt[3]{ - 375} = \sqrt[3]{ - 3 \times 5 \times 5 \times 5} = - \sqrt[3]{ 3 \times 125} = - 5 \sqrt[3]{ 3} [/tex]
[tex] \sqrt[3]{ - 3645} = \sqrt[3]{ - 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 5} = - \sqrt[3]{27 \times 27 \times 5} = - \sqrt[3]{729 \times 5} = - 9 \sqrt[3]{5} [/tex]
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