1) $\frac{3}{\sqrt{2}} = \frac{3\sqrt{2}}{2}$
2) $\frac{11}{\sqrt{5}} = \frac{11\sqrt{5}}{5}$
3) $\frac{9}{\sqrt{7}} = \frac{9\sqrt{7}}{7}$
4) $\frac{4}{\sqrt{11}} = \frac{4\sqrt{11}}{11}$
5) $\frac{20}{\sqrt{13}} = \frac{20\sqrt{13}}{13}$
6) $\frac{15}{\sqrt{3}} = \frac{15\sqrt{3}}{3} = 5\sqrt{3}$
7) $\frac{14}{\sqrt{2}} = \frac{14\sqrt{2}}{2} = 7\sqrt{2}$
8) $\frac{20}{\sqrt{5}} = \frac{20\sqrt{5}}{5} = 4\sqrt{5}$
9) $\frac{22}{\sqrt{11}} = \frac{22\sqrt{11}}{11} = 2\sqrt{11}$
10) $\frac{8}{\sqrt{6}} = \frac{8\sqrt{6}}{6} = \frac{4\sqrt{6}}{3}$
11) $\frac{28}{3\sqrt{7}} = \frac{28\sqrt{7}}{3 \cdot 7} = \frac{28\sqrt{7}}{21} = \frac{4\sqrt{7}}{3}$
12) $\frac{18}{5\sqrt{3}} = \frac{18\sqrt{3}}{5 \cdot 3} = \frac{18\sqrt{3}}{15} = \frac{6\sqrt{3}}{5}$
13) $\frac{2}{7\sqrt{4}} = \frac{2}{7 \cdot 2} = \frac{2}{14} = \frac{1}{7}$
14) $\frac{25}{3\sqrt{5}} = \frac{25\sqrt{5}}{3 \cdot 5} = \frac{25\sqrt{5}}{15} = \frac{5\sqrt{5}}{3}$
15) $\frac{54}{9\sqrt{2}} = \frac{54\sqrt{2}}{9 \cdot 2} = \frac{54\sqrt{2}}{18} = 3\sqrt{2}$
16) $\frac{\sqrt{27}}{\sqrt{3}} = \sqrt{\frac{27}{3}} = \sqrt{9} = 3$
17) $\frac{\sqrt{75}}{\sqrt{3}} = \sqrt{\frac{75}{3}} = \sqrt{25} = 5$
18) $\frac{\sqrt{64}}{\sqrt{4}} = \frac{8}{2} = 4$
19) $\frac{\sqrt{98}}{\sqrt{2}} = \sqrt{\frac{98}{2}} = \sqrt{49} = 7$
20) $\frac{\sqrt{24}}{\sqrt{6}} = \sqrt{\frac{24}{6}} = \sqrt{4} = 2$
1) $\frac{11}{2 - \sqrt{3}} = \frac{11(2 + \sqrt{3})}{(2 - \sqrt{3})(2 + \sqrt{3})} = \frac{11(2 + \sqrt{3})}{4 - 3} = 11(2 + \sqrt{3}) = 22 + 11\sqrt{3}$
2) $\frac{1}{2 - \sqrt{5}} = \frac{1(2 + \sqrt{5})}{(2 - \sqrt{5})(2 + \sqrt{5})} = \frac{2 + \sqrt{5}}{4 - 5} = \frac{2 + \sqrt{5}}{-1} = -2 - \sqrt{5}$
3) $\frac{12}{3 - \sqrt{3}} = \frac{12(3 + \sqrt{3})}{(3 - \sqrt{3})(3 + \sqrt{3})} = \frac{12(3 + \sqrt{3})}{9 - 3} = \frac{12(3 + \sqrt{3})}{6} = 2(3 + \sqrt{3}) = 6 + 2\sqrt{3}$
4) $\frac{7}{1 + \sqrt{2}} = \frac{7(1 - \sqrt{2})}{(1 + \sqrt{2})(1 - \sqrt{2})} = \frac{7(1 - \sqrt{2})}{1 - 2} = \frac{7(1 - \sqrt{2})}{-1} = -7 + 7\sqrt{2}$
5) $\frac{4}{3 + \sqrt{11}} = \frac{4(3 - \sqrt{11})}{(3 + \sqrt{11})(3 - \sqrt{11})} = \frac{4(3 - \sqrt{11})}{9 - 11} = \frac{4(3 - \sqrt{11})}{-2} = -2(3 - \sqrt{11}) = -6 + 2\sqrt{11}$
6) $\frac{1}{\sqrt{3} - 1} = \frac{1(\sqrt{3} + 1)}{(\sqrt{3} - 1)(\sqrt{3} + 1)} = \frac{\sqrt{3} + 1}{3 - 1} = \frac{\sqrt{3} + 1}{2}$
Parent Tip: Review the logic above to help your child master the concept of simplifying radicals worksheet algebra 1.
