Wortels vereenvoudigen
2i - 11 oefeningen
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BreukInWortel (1)
008b - basis
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Getal & Ruimte (13e editie) - 3 havo - 5.4 Getal & Ruimte (13e editie) - 2 vwo - 5.3 |
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Herleid. 1p a \(\sqrt{7\frac{1}{9}}\) |
a \(\sqrt{7\frac{1}{9}}=\sqrt{\frac{64}{9}}={\sqrt{64} \over \sqrt{9}}=\frac{8}{3}=2\frac{2}{3}\text{.}\) 1p |
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BreukInWortel (2)
008c - basis
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Getal & Ruimte (13e editie) - 3 havo - 5.4 Getal & Ruimte (13e editie) - 3 vwo - 5.5 |
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Herleid. 1p a \(\sqrt{\frac{19}{25}}\) |
a \(\sqrt{\frac{19}{25}}={\sqrt{19} \over \sqrt{25}}={\sqrt{19} \over 5}=\frac{1}{5}\sqrt{19}\text{.}\) 1p |
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BreukInWortel (3)
008d - basis
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Getal & Ruimte (12e editie) - havo wiskunde B - 3.3 Getal & Ruimte (13e editie) - 3 vwo - 5.5 |
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Herleid. 1p a \(\sqrt{1\frac{27}{73}}\) |
a \(\sqrt{1\frac{27}{73}}=\sqrt{\frac{100}{73}}={\sqrt{100} \over \sqrt{73}}={10 \over \sqrt{73}}⋅{\sqrt{73} \over \sqrt{73}}={10\sqrt{73} \over 73}=\frac{10}{73}\sqrt{73}\text{.}\) 1p |
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BreukInWortel (4)
008e - basis
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Getal & Ruimte (12e editie) - havo wiskunde B - 3.3 Getal & Ruimte (13e editie) - 3 vwo - 5.5 |
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Herleid. 1p a \(\sqrt{\frac{7}{12}}\) |
a \(\sqrt{\frac{7}{12}}={\sqrt{7} \over \sqrt{12}}⋅{\sqrt{12} \over \sqrt{12}}={\sqrt{84} \over 12}=\frac{1}{12}\sqrt{84}=\frac{1}{12}⋅2⋅\sqrt{21}=\frac{1}{6}\sqrt{21}\text{.}\) 1p |
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Delen (4)
00dc - basis
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Getal & Ruimte (13e editie) - 3 vwo - 5.5 |
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Herleid. 1p a \({6\sqrt{400} \over 3\sqrt{10}}\) |
a \({6\sqrt{400} \over 3\sqrt{10}}={6 \over 3}⋅{\sqrt{400} \over \sqrt{10}}=2\sqrt{40}=2⋅\sqrt{4}⋅\sqrt{10}=2⋅2⋅\sqrt{10}=4\sqrt{10}\) 1p |
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FactorVoorWortelteken (1)
0086 - basis
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Getal & Ruimte (13e editie) - 2 havo/vwo - 5.3 Getal & Ruimte (13e editie) - 2 vwo - 5.3 |
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Herleid. 1p a \(\sqrt{20}\) |
a \(\sqrt{20}=\sqrt{4}⋅\sqrt{5}=2\sqrt{5}\text{.}\) 1p |
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FactorVoorWortelteken (2)
0087 - basis
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Getal & Ruimte (13e editie) - 2 havo/vwo - 5.3 Getal & Ruimte (13e editie) - 2 vwo - 5.3 |
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Herleid. 1p a \(5\sqrt{18}\) |
a \(5\sqrt{18}=5⋅\sqrt{9}⋅\sqrt{2}=5⋅3⋅\sqrt{2}=15\sqrt{2}\text{.}\) 1p |
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Optellen (5)
0085 - basis
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Getal & Ruimte (12e editie) - havo wiskunde B - 3.3 Getal & Ruimte (13e editie) - 2 vwo - 5.3 |
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Herleid. 2p a \(\sqrt{32}+\sqrt{8}\) |
a \(\sqrt{32}+\sqrt{8}=\sqrt{16}⋅\sqrt{2}+\sqrt{4}⋅\sqrt{2}=4\sqrt{2}+2\sqrt{2}\text{.}\) 1p \(4\sqrt{2}+2\sqrt{2}=6\sqrt{2}\text{.}\) 1p |
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Optellen (6)
0088 - basis
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Getal & Ruimte (12e editie) - havo wiskunde B - 3.3 Getal & Ruimte (13e editie) - 2 vwo - 5.3 |
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Herleid. 2p a \(3\sqrt{125}+4\sqrt{80}\) |
a \(3\sqrt{125}+4\sqrt{80}=3⋅\sqrt{25}⋅\sqrt{5}+4⋅\sqrt{16}⋅\sqrt{5}\text{.}\) 1p \(3⋅5⋅\sqrt{5}+4⋅4⋅\sqrt{5}=15\sqrt{5}+16\sqrt{5}=31\sqrt{5}\text{.}\) 1p |
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Vermenigvuldigen (5)
00dd - basis - data pool: #22 (2ms)
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Getal & Ruimte (13e editie) - 3 vwo - 5.5 |
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Herleid. 1p a \(4\sqrt{2}⋅3\sqrt{6}\) |
a \(4\sqrt{2}⋅3\sqrt{6}=12\sqrt{12}=12⋅\sqrt{4}⋅\sqrt{3}=12⋅2⋅\sqrt{3}=24\sqrt{3}\) 1p |
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WortelInNoemer
0089 - basis
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Getal & Ruimte (12e editie) - havo wiskunde B - 3.3 Getal & Ruimte (13e editie) - 3 vwo - 5.5 |
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Herleid. 1p a \({5 \over 4\sqrt{7}}\) |
a \({5 \over 4\sqrt{7}}={5 \over 4\sqrt{7}}⋅{\sqrt{7} \over \sqrt{7}}={5\sqrt{7} \over 4⋅7}=\frac{5}{28}\sqrt{7}\text{.}\) 1p |