Rekenen met wortels (reeks 5)

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Maak de noemer wortelvrij

1. \(\frac{36}{\sqrt{2}}\)
2. \(\frac{55}{\sqrt{8}}\)
3. \(\frac{51}{\sqrt{15}}\)
4. \(\frac{5}{\sqrt{5}}\)
5. \(\frac{9}{\sqrt{2}}\)
6. \(\frac{50}{\sqrt{13}}\)
7. \(\frac{54}{\sqrt{2}}\)
8. \(\frac{25}{\sqrt{15}}\)
9. \(\frac{30}{\sqrt{2}}\)
10. \(\frac{21}{\sqrt{14}}\)
11. \(\frac{44}{\sqrt{5}}\)
12. \(\frac{46}{\sqrt{5}}\)

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Maak de noemer wortelvrij

Verbetersleutel

1. \(\frac{36}{\sqrt{2}}=\frac{36\cdot \color{red}{\sqrt{2}} }{\sqrt{2}\cdot \color{red}{\sqrt{2}} }=\frac{36\cdot\sqrt{2}}{2}=18\cdot\sqrt{2}\)
2. \(\frac{55}{\sqrt{8}}=\frac{55\cdot \color{red}{\sqrt{8}} }{\sqrt{8}\cdot \color{red}{\sqrt{8}} }=\frac{55\cdot\sqrt{8}}{8}\)
3. \(\frac{51}{\sqrt{15}}=\frac{51\cdot \color{red}{\sqrt{15}} }{\sqrt{15}\cdot \color{red}{\sqrt{15}} }=\frac{51\cdot\sqrt{15}}{15}=\frac{17\cdot\sqrt{15}}{5}\)
4. \(\frac{5}{\sqrt{5}}=\frac{5\cdot \color{red}{\sqrt{5}} }{\sqrt{5}\cdot \color{red}{\sqrt{5}} }=\frac{5\cdot\sqrt{5}}{5}=\frac{\sqrt{5}}{1}\)
5. \(\frac{9}{\sqrt{2}}=\frac{9\cdot \color{red}{\sqrt{2}} }{\sqrt{2}\cdot \color{red}{\sqrt{2}} }=\frac{9\cdot\sqrt{2}}{2}\)
6. \(\frac{50}{\sqrt{13}}=\frac{50\cdot \color{red}{\sqrt{13}} }{\sqrt{13}\cdot \color{red}{\sqrt{13}} }=\frac{50\cdot\sqrt{13}}{13}\)
7. \(\frac{54}{\sqrt{2}}=\frac{54\cdot \color{red}{\sqrt{2}} }{\sqrt{2}\cdot \color{red}{\sqrt{2}} }=\frac{54\cdot\sqrt{2}}{2}=27\cdot\sqrt{2}\)
8. \(\frac{25}{\sqrt{15}}=\frac{25\cdot \color{red}{\sqrt{15}} }{\sqrt{15}\cdot \color{red}{\sqrt{15}} }=\frac{25\cdot\sqrt{15}}{15}=\frac{5\cdot\sqrt{15}}{3}\)
9. \(\frac{30}{\sqrt{2}}=\frac{30\cdot \color{red}{\sqrt{2}} }{\sqrt{2}\cdot \color{red}{\sqrt{2}} }=\frac{30\cdot\sqrt{2}}{2}=15\cdot\sqrt{2}\)
10. \(\frac{21}{\sqrt{14}}=\frac{21\cdot \color{red}{\sqrt{14}} }{\sqrt{14}\cdot \color{red}{\sqrt{14}} }=\frac{21\cdot\sqrt{14}}{14}=\frac{3\cdot\sqrt{14}}{2}\)
11. \(\frac{44}{\sqrt{5}}=\frac{44\cdot \color{red}{\sqrt{5}} }{\sqrt{5}\cdot \color{red}{\sqrt{5}} }=\frac{44\cdot\sqrt{5}}{5}\)
12. \(\frac{46}{\sqrt{5}}=\frac{46\cdot \color{red}{\sqrt{5}} }{\sqrt{5}\cdot \color{red}{\sqrt{5}} }=\frac{46\cdot\sqrt{5}}{5}\)