[tex]a) \ \sqrt{16+9} \ \ i \ \ \sqrt{16}+\sqrt{4}\\\\\sqrt{16+9} = \sqrt{25} = 5\\\\\sqrt{16}+\sqrt{4} = 4+2 = 2\\\\5 < 6\\\\\boxed{\sqrt{16+9} < \sqrt{16}+\sqrt{4}}[/tex]
[tex]b) \ \sqrt{25-9} \ \ i \ \ \sqrt{25}-\sqrt{9}\\\\\sqrt{25-9} = \sqrt{16} = 4\\\\\sqrt{25}-\sqrt{9} = 5-3 = 2\\\\4 > 2\\\\\boxed{\sqrt{25-9} > \sqrt{25}-\sqrt{9}}[/tex]
[tex]c) \ 2\sqrt{7} \ \ i \ \ \sqrt{3\cdot7}\\\\2\sqrt{7} = \sqrt{2^{2}\cdot7} = \sqrt{4\cdot7}\\\\\sqrt{4\cdot7} > \sqrt{3\cdot7}\\\\\boxed{2\sqrt{7} > \sqrt{3\cdot7}}[/tex]
