Rekenen met wortels (reeks 5)

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Maak de noemer wortelvrij

1. \(\frac{24}{\sqrt{3}}\)
2. \(\frac{14}{\sqrt{8}}\)
3. \(\frac{17}{\sqrt{5}}\)
4. \(\frac{13}{\sqrt{8}}\)
5. \(\frac{53}{\sqrt{15}}\)
6. \(\frac{20}{\sqrt{14}}\)
7. \(\frac{32}{\sqrt{17}}\)
8. \(\frac{53}{\sqrt{7}}\)
9. \(\frac{52}{\sqrt{14}}\)
10. \(\frac{34}{\sqrt{6}}\)
11. \(\frac{30}{\sqrt{10}}\)
12. \(\frac{44}{\sqrt{3}}\)

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Maak de noemer wortelvrij

Verbetersleutel

1. \(\frac{24}{\sqrt{3}}=\frac{24\cdot \color{red}{\sqrt{3}} }{\sqrt{3}\cdot \color{red}{\sqrt{3}} }=\frac{24\cdot\sqrt{3}}{3}=8\cdot\sqrt{3}\)
2. \(\frac{14}{\sqrt{8}}=\frac{14\cdot \color{red}{\sqrt{8}} }{\sqrt{8}\cdot \color{red}{\sqrt{8}} }=\frac{14\cdot\sqrt{8}}{8}=\frac{7\cdot\sqrt{8}}{4}\)
3. \(\frac{17}{\sqrt{5}}=\frac{17\cdot \color{red}{\sqrt{5}} }{\sqrt{5}\cdot \color{red}{\sqrt{5}} }=\frac{17\cdot\sqrt{5}}{5}\)
4. \(\frac{13}{\sqrt{8}}=\frac{13\cdot \color{red}{\sqrt{8}} }{\sqrt{8}\cdot \color{red}{\sqrt{8}} }=\frac{13\cdot\sqrt{8}}{8}\)
5. \(\frac{53}{\sqrt{15}}=\frac{53\cdot \color{red}{\sqrt{15}} }{\sqrt{15}\cdot \color{red}{\sqrt{15}} }=\frac{53\cdot\sqrt{15}}{15}\)
6. \(\frac{20}{\sqrt{14}}=\frac{20\cdot \color{red}{\sqrt{14}} }{\sqrt{14}\cdot \color{red}{\sqrt{14}} }=\frac{20\cdot\sqrt{14}}{14}=\frac{10\cdot\sqrt{14}}{7}\)
7. \(\frac{32}{\sqrt{17}}=\frac{32\cdot \color{red}{\sqrt{17}} }{\sqrt{17}\cdot \color{red}{\sqrt{17}} }=\frac{32\cdot\sqrt{17}}{17}\)
8. \(\frac{53}{\sqrt{7}}=\frac{53\cdot \color{red}{\sqrt{7}} }{\sqrt{7}\cdot \color{red}{\sqrt{7}} }=\frac{53\cdot\sqrt{7}}{7}\)
9. \(\frac{52}{\sqrt{14}}=\frac{52\cdot \color{red}{\sqrt{14}} }{\sqrt{14}\cdot \color{red}{\sqrt{14}} }=\frac{52\cdot\sqrt{14}}{14}=\frac{26\cdot\sqrt{14}}{7}\)
10. \(\frac{34}{\sqrt{6}}=\frac{34\cdot \color{red}{\sqrt{6}} }{\sqrt{6}\cdot \color{red}{\sqrt{6}} }=\frac{34\cdot\sqrt{6}}{6}=\frac{17\cdot\sqrt{6}}{3}\)
11. \(\frac{30}{\sqrt{10}}=\frac{30\cdot \color{red}{\sqrt{10}} }{\sqrt{10}\cdot \color{red}{\sqrt{10}} }=\frac{30\cdot\sqrt{10}}{10}=3\cdot\sqrt{10}\)
12. \(\frac{44}{\sqrt{3}}=\frac{44\cdot \color{red}{\sqrt{3}} }{\sqrt{3}\cdot \color{red}{\sqrt{3}} }=\frac{44\cdot\sqrt{3}}{3}\)