[tex]5\sqrt{5} =\sqrt{5^2*5}=\sqrt{5^3} =\sqrt{125} \\2\sqrt{6} =\sqrt{2^2*6} =\sqrt{4*6} =\sqrt{24} \\13\sqrt{2} =\sqrt{13^2*2} =\sqrt{169*2} =\sqrt{338} \\3\sqrt{5} =\sqrt{3^2*5} =\sqrt{9*5}=\sqrt{45} \\9\sqrt{6} =\sqrt{9^2*6} =\sqrt{81*6}=\sqrt{486} \\2\sqrt{3} =\sqrt{2^2*3} =\sqrt{4*3} =\sqrt{12} \\4\sqrt{4} =\sqrt{4^2*4} =\sqrt{4^3} =\sqrt{64}[/tex]
