[tex]a) \ \sqrt{2}\cdot\sqrt{72} = \sqrt{2\cdot72} = \sqrt{144} = \sqrt{12^{2}} 12\\\\b) \ \frac{\sqrt{63}}{\sqrt{7}} = \sqrt{\frac{63}{7}} = \sqrt{9} = \sqrt{3^{2}} = 3\\\\c) \ \sqrt[3]{4}\cdot\sqrt[3]{-54} = \sqrt[3]{4\cdot(-54)} = \sqrt[3]{-216} = \sqrt[3]{(-16)^{3}} = -16[/tex]
[tex]d) \ \sqrt{9}+\sqrt{16} = \sqrt{3^{2}}+\sqrt{4^{2}} = 3+4 = 7\\\\e) \ \frac{\sqrt[3]{1250}}{\sqrt[3]{10}} = \sqrt[3]{\frac{1250}{10}} = \sqrt[3]{125} = \sqrt[3]{5^{3}} =5\\\\f) \ \sqrt{169}-\sqrt{144} = \sqrt{13^{2}}-\sqrt{12^{2}} = 13-12 = 1[/tex]
