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 \(\sqrt{1\frac{13}{36}}\) |
a \(\sqrt{1\frac{13}{36}}=\sqrt{\frac{49}{36}}={\sqrt{49} \over \sqrt{36}}=\frac{7}{6}=1\frac{1}{6}\text{.}\) 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 \(\sqrt{\frac{5}{49}}\) |
a \(\sqrt{\frac{5}{49}}={\sqrt{5} \over \sqrt{49}}={\sqrt{5} \over 7}=\frac{1}{7}\sqrt{5}\text{.}\) 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 \(\sqrt{1\frac{7}{18}}\) |
a \(\sqrt{1\frac{7}{18}}=\sqrt{\frac{25}{18}}={\sqrt{25} \over \sqrt{18}}={5 \over \sqrt{18}}⋅{\sqrt{18} \over \sqrt{18}}={5\sqrt{18} \over 18}=\frac{5}{18}\sqrt{18}=\frac{5}{18}⋅3⋅\sqrt{2}=\frac{5}{6}\sqrt{2}\text{.}\) 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 \(\sqrt{\frac{2}{41}}\) |
a \(\sqrt{\frac{2}{41}}={\sqrt{2} \over \sqrt{41}}⋅{\sqrt{41} \over \sqrt{41}}={\sqrt{82} \over 41}=\frac{1}{41}\sqrt{82}\text{.}\) 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 \({21\sqrt{280} \over 7\sqrt{10}}\) |
a \({21\sqrt{280} \over 7\sqrt{10}}={21 \over 7}⋅{\sqrt{280} \over \sqrt{10}}=3\sqrt{28}=3⋅\sqrt{4}⋅\sqrt{7}=3⋅2⋅\sqrt{7}=6\sqrt{7}\) 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 \(\sqrt{50}\) |
a \(\sqrt{50}=\sqrt{25}⋅\sqrt{2}=5\sqrt{2}\text{.}\) 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 \(-3\sqrt{28}\) |
a \(-3\sqrt{28}=-3⋅\sqrt{4}⋅\sqrt{7}=-3⋅2⋅\sqrt{7}=-6\sqrt{7}\text{.}\) 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 \(\sqrt{32}+\sqrt{200}\) |
a \(\sqrt{32}+\sqrt{200}=\sqrt{16}⋅\sqrt{2}+\sqrt{100}⋅\sqrt{2}=4\sqrt{2}+10\sqrt{2}\text{.}\) 1p \(4\sqrt{2}+10\sqrt{2}=14\sqrt{2}\text{.}\) 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 \(5\sqrt{48}+7\sqrt{27}\) |
a \(5\sqrt{48}+7\sqrt{27}=5⋅\sqrt{16}⋅\sqrt{3}+7⋅\sqrt{9}⋅\sqrt{3}\text{.}\) 1p \(5⋅4⋅\sqrt{3}+7⋅3⋅\sqrt{3}=20\sqrt{3}+21\sqrt{3}=41\sqrt{3}\text{.}\) 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 \(2\sqrt{6}⋅3\sqrt{14}\) |
a \(2\sqrt{6}⋅3\sqrt{14}=6\sqrt{84}=6⋅\sqrt{4}⋅\sqrt{21}=6⋅2⋅\sqrt{21}=12\sqrt{21}\) 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 \({3 \over 5\sqrt{5}}\) |
a \({3 \over 5\sqrt{5}}={3 \over 5\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={3\sqrt{5} \over 5⋅5}=\frac{3}{25}\sqrt{5}\text{.}\) 1p |