32.
[tex]a) \ \sqrt{36}-\sqrt[3]{-8}=\sqrt{36}-(-\sqrt[3]{8}) = \sqrt{36}+\sqrt[3]{8} = \sqrt{6^{2}}+\sqrt[3]{2^{3}} = 6+2 = \boxed{8}\\\\b) \ 4\sqrt{\frac{1}{64}}+\frac{\sqrt{16}}{2} = 4\cdot\frac{1}{8}+\frac{4}{2} =\frac{1}{2}+2 = \boxed{2\frac{1}{2}}\\\\c) \ \sqrt[3]{25\cdot\sqrt{25}} = \sqrt[3]{5^{2}\cdot5} = \sqrt[3]{5^{3}} =\boxed{ 5}\\\\d) \ \sqrt{9\sqrt{9\sqrt{81}}} = \sqrt{9\sqrt{9\cdot9}} = \sqrt{9\cdot9} = \boxed{9}[/tex]
[tex]e) \ \sqrt{144}+\sqrt{25}-\sqrt{144+25} = 12+5-\sqrt{169} = 17-13 = \boxed{4}\\\\f) \ \sqrt{100}:\sqrt[3]{8}+\sqrt{49} = 10:2+7 = 5+7 = \boxed{12}[/tex]
