$\text{a)}\sqrt{1\frac{24}{25}}=\sqrt{\frac{49}{25}}=\frac{\sqrt{49}}{\sqrt{25}}=\frac{7}{5}=1\frac{2}{5}$  

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$\text{b)}\sqrt{3\frac{13}{81}}=\sqrt{\frac{256}{81}}=\frac{\sqrt{256}}{\sqrt{81}}=\frac{16}{9}=1\frac{7}{9}$  

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$\text{c)}\sqrt{3,61}=\sqrt{3\frac{61}{100}}=\sqrt{\frac{361}{100}}=\frac{\sqrt{361}}{\sqrt{100}}=\frac{19}{10}=1,9$  

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$\text{d)}\sqrt{2,25}=\sqrt{2\frac{25}{100}}=\sqrt{\frac{225}{100}}=\frac{\sqrt{225}}{\sqrt{100}}=\frac{15}{10}=1,5$  

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$\text{e)}\sqrt{3}\cdot \sqrt{27}=\sqrt{3\cdot 27}=\sqrt{81}=9$  

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$\text{f)}\sqrt{6}\cdot \sqrt{24}=\sqrt{6\cdot 24}=\sqrt{144}=12$