[tex]\sqrt{12} = \sqrt{4\cdot 3} = \sqrt{2^2\cdot 3} = \sqrt{2^2}\cdot \sqrt{3} = 2\sqrt{3}[/tex]
[tex]\sqrt{18} = \sqrt{9\cdot 2} = \sqrt{3^2\cdot 2} = \sqrt{3^2}\cdot \sqrt{2} = 3\sqrt{2}[/tex]
[tex]\sqrt{27} = \sqrt{9\cdot 3} = \sqrt{3^2\cdot 3} = \sqrt{3^2}\cdot \sqrt{3} = 3\sqrt{3}[/tex]
[tex]\sqrt{32} = \sqrt{16\cdot 2} = \sqrt{4^2\cdot 2} = \sqrt{4^2}\cdot 2 = 4\sqrt{2}[/tex]
[tex]\sqrt{75} = \sqrt{25\cdot 3} = \sqrt{5^2\cdot 3} = \sqrt{5^2}\cdot \sqrt{3} = 5\sqrt{3}[/tex]
[tex]\sqrt{98} = \sqrt{49\cdot 2} = \sqrt{7^2\cdot 2} = \sqrt{7^2}\cdot \sqrt{2} = 7\sqrt{2}[/tex]