Wortels vereenvoudigen

\(\sqrt{\frac{25}{36}} = {\sqrt{25} \over \sqrt{36}} = \frac{5}{6} \text{.}\)

\(\sqrt{\frac{44}{81}} = {\sqrt{44} \over \sqrt{81}} = {\sqrt{44} \over 9} = \frac{1}{9} \sqrt{44} = \frac{1}{9} ⋅ 2 ⋅ \sqrt{11} = \frac{2}{9} \sqrt{11} \text{.}\)

\(\sqrt{1\frac{23}{58}} = \sqrt{\frac{81}{58}} = {\sqrt{81} \over \sqrt{58}} = {9 \over \sqrt{58}} ⋅ {\sqrt{58} \over \sqrt{58}} = {9 \sqrt{58} \over 58} = \frac{9}{58} \sqrt{58} \text{.}\)

\(\sqrt{16\frac{1}{2}} = \sqrt{\frac{33}{2}} = {\sqrt{33} \over \sqrt{2}} ⋅ {\sqrt{2} \over \sqrt{2}} = {\sqrt{66} \over 2} = \frac{1}{2} \sqrt{66} \text{.}\)

\({5 \sqrt{144} \over \sqrt{6}} = 5 ⋅ {\sqrt{144} \over \sqrt{6}} = 5 \sqrt{24} = 5 ⋅ \sqrt{4} ⋅ \sqrt{6} = 5 ⋅ 2 ⋅ \sqrt{6} = 10 \sqrt{6}\)

\(\sqrt{500} = \sqrt{100} ⋅ \sqrt{5} = 10 \sqrt{5} \text{.}\)

\(-5 \sqrt{8} = -5 ⋅ \sqrt{4} ⋅ \sqrt{2} = -5 ⋅ 2 ⋅ \sqrt{2} = -10 \sqrt{2} \text{.}\)

\(\sqrt{48} + \sqrt{75} = \sqrt{16} ⋅ \sqrt{3} + \sqrt{25} ⋅ \sqrt{3} = 4 \sqrt{3} + 5 \sqrt{3} \text{.}\)

\(4 \sqrt{3} + 5 \sqrt{3} = 9 \sqrt{3} \text{.}\)

\(3 \sqrt{18} + 7 \sqrt{8} = 3 ⋅ \sqrt{9} ⋅ \sqrt{2} + 7 ⋅ \sqrt{4} ⋅ \sqrt{2} \text{.}\)

\(3 ⋅ 3 ⋅ \sqrt{2} + 7 ⋅ 2 ⋅ \sqrt{2} = 9 \sqrt{2} + 14 \sqrt{2} = 23 \sqrt{2} \text{.}\)

\({-3 \over 1 + \sqrt{6}} = {-3 \over 1 + \sqrt{6}} ⋅ {1 - \sqrt{6} \over 1 - \sqrt{6}}\)
\(\text{} = {-3 (1 + \sqrt{6}) \over 1 - 6}\)
\(\text{} = \frac{3}{5} (1 + \sqrt{6})\)
\(\text{} = \frac{3}{5} + \frac{3}{5} \sqrt{6}\)

\({4 \sqrt{5} \over \sqrt{6} - \sqrt{3}} = {4 \sqrt{5} \over \sqrt{6} - \sqrt{3}} ⋅ {\sqrt{6} + \sqrt{3} \over \sqrt{6} + \sqrt{3}}\)
\(\text{} = {4 \sqrt{5} (\sqrt{6} + \sqrt{3}) \over 6 - 3}\)
\(\text{} = 1\frac{1}{3} \sqrt{5} (\sqrt{6} + \sqrt{3})\)
\(\text{} = 1\frac{1}{3} \sqrt{30} + 1\frac{1}{3} \sqrt{15}\)

\(5 \sqrt{3} ⋅ 4 \sqrt{15} = 20 \sqrt{45} = 20 ⋅ \sqrt{9} ⋅ \sqrt{5} = 20 ⋅ 3 ⋅ \sqrt{5} = 60 \sqrt{5}\)

\({9 \over 2 \sqrt{7}} = {9 \over 2 \sqrt{7}} ⋅ {\sqrt{7} \over \sqrt{7}} = {9 \sqrt{7} \over 2 ⋅ 7} = \frac{9}{14} \sqrt{7} \text{.}\)