(1) 54=6⋅32=36\sqrt{54} = \sqrt{6 \cdot 3^2} = 3\sqrt{6}54=6⋅32=36 (2) 63=7⋅32=37\sqrt{63} = \sqrt{7 \cdot 3^2} = 3\sqrt{7}63=7⋅32=37 (3) 1225=3⋅2252=253\sqrt{\frac{12}{25}} = \sqrt{\frac{3 \cdot 2^2}{5^2}} = \frac{2}{5}\sqrt{3}2512=523⋅22=523 (4) 8+18=23+2⋅32=22+32\sqrt{8} + \sqrt{18} = \sqrt{2^3} + \sqrt{2 \cdot 3^2} = 2\sqrt{2} + 3\sqrt{2}8+18=23+2⋅32=22+32 (5) 50−32−18=2⋅52−2⋅42−2⋅32=52−42−32=−22\sqrt{50} - \sqrt{32} - \sqrt{18} = \sqrt{2 \cdot 5^2} - \sqrt{2 \cdot 4^2} - \sqrt{2 \cdot 3^2} = 5\sqrt{2} - 4\sqrt{2} - 3\sqrt{2} = -2\sqrt{2}50−32−18=2⋅52−2⋅42−2⋅32=52−42−32=−22