6.
[tex]a) \ \sqrt{81}-\sqrt[3]{-27} = 9-(-3) = 9+3 = 12\\\\b) \ 2\sqrt{\frac{1}{36}}+\frac{\sqrt{144}}{4} = 2\cdot\frac{1}{6}+\frac{12}{4}=\frac{1}{3}+3 = 3\frac{1}{3}\\\\c) \ \sqrt[3]{100\cdot\sqrt{100}} = \sqrt[3]{100\cdot10} = \sqrt[3]{1000} = 10[/tex]
[tex]d) \ \sqrt{5\sqrt{5\sqrt{25}}} = \sqrt{5\sqrt{5\cdot5}} = \sqrt{5\cdot5} = 5\\\\e) \ \sqrt{169}-\sqrt{25}+\sqrt{169-25} = 13-5+\sqrt{144} = 8+12 = 20\\\\f) \ \sqrt{1600}:\sqrt[3]{64}+\sqrt{9} = 40:4+3 = 10+3 = 13[/tex]
7.
[tex]a) \ 4(\sqrt{5})^{2} =4\cdot5 = 20\\\\b) \ 3\sqrt{10}\cdot2\sqrt{10} = 6\sqrt{10\cdot10} = 6\cdot10 = 60\\\\c) \ (\frac{5}{6}\sqrt{3})^{2} = (\frac{5}{6})^{2}\cdot(\sqrt{3})^{2} = \frac{25}{36}\cdot3 = \frac{25}{12} = 2\frac{1}{12}[/tex]
