Verified answer

[tex]1.[/tex]

[tex]a) \: \: \: \: \: \sqrt{12} \times \sqrt{3} = \sqrt{12 \times 3} = \sqrt{36} = 6[/tex]

[tex]b) \: \: \: \: \: \frac{ \sqrt{2.8} }{ \sqrt{0.7} } = \sqrt{ \frac{2.8}{0.7} } = \sqrt{4} = 2 \\ [/tex]

[tex]( { \sqrt{21} })^{2} = 21[/tex]

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[tex]2.[/tex]

[tex]4 \sqrt{18b} - 2 \sqrt{32b} + 3 \sqrt{800b} = \sqrt{16 \times 18b} - \sqrt{4 \times 32b} + \sqrt{9 \times 800b} = \sqrt{288b} - \sqrt{128b} + \sqrt{7200b} = \sqrt{2 b\times 144} - \sqrt{2 b\times 64} + \sqrt{2b \times 3600} = 12 \sqrt{2b} - 8 \sqrt{2b} + 60 \sqrt{2b} = 64 \sqrt{2b} [/tex]

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[tex]3. \: \: \: \: \: 3 \sqrt{6} \: ; \: 2 \sqrt{13} \: ; \: 4 \sqrt{3} \: ; \: \sqrt{26} [/tex]

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[tex]4. \: \: \: \: \: (7 \sqrt{2} - \sqrt{98} + \sqrt{10} ) \times \sqrt{2} = (7 \sqrt{2} - \sqrt{49 \times 2} + \sqrt{10} ) \times \sqrt{2} = (7 \sqrt{2} - 7 \sqrt{2} + \sqrt{10} ) \times \sqrt{2} = \sqrt{10} \times \sqrt{2} = \sqrt{10 \times 2} = \sqrt{20} = \sqrt{4 \times 5} = 2 \sqrt{5} [/tex]

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[tex] \frac{4a}{ \sqrt{11} } = {( \frac{4a}{ \sqrt{11} } })^{2} = \frac{ {(4a)}^{2} }{ { \sqrt{11} }^{2} } = \frac{16 {a}^{2} }{11} \\ [/tex]

[tex] \frac{3}{ \sqrt{7} - 2 } = \frac{3( \sqrt{7} + 2)}{( \sqrt{7} - 2)( \sqrt{7} + 2) } = \frac{3 \sqrt{7} + 6 }{7 - 4} = \frac{3 \sqrt{7} + 6}{3} = \frac{3( \sqrt{7} + 2)}{3} = \sqrt{7} + 2[/tex]