Wortels vereenvoudigen
2i - 13 oefeningen
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BreukInWortel (1)
008b - Wortels vereenvoudigen - basis - 47ms
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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 \(\sqrt{\frac{4}{49}}\) |
○ \(\sqrt{\frac{4}{49}} = {\sqrt{4} \over \sqrt{49}} = \frac{2}{7} \text{.}\) 1p |
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BreukInWortel (2)
008c - Wortels vereenvoudigen - basis - 1ms
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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 \(\sqrt{1\frac{8}{25}}\) |
○ \(\sqrt{1\frac{8}{25}} = \sqrt{\frac{33}{25}} = {\sqrt{33} \over \sqrt{25}} = {\sqrt{33} \over 5} = \frac{1}{5} \sqrt{33} \text{.}\) 1p |
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BreukInWortel (3)
008d - Wortels vereenvoudigen - basis - 1ms
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Getal & Ruimte (12e editie) - havo wiskunde B - 3.3 Getal & Ruimte (13e editie) - 3 vwo - 5.5 Getal & Ruimte (13e editie) - havo wiskunde B - 7.2 |
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Herleid. 1p \(\sqrt{\frac{49}{52}}\) |
○ \(\sqrt{\frac{49}{52}} = {\sqrt{49} \over \sqrt{52}} = {7 \over \sqrt{52}} ⋅ {\sqrt{52} \over \sqrt{52}} = {7 \sqrt{52} \over 52} = \frac{7}{52} \sqrt{52} = \frac{7}{52} ⋅ 2 ⋅ \sqrt{13} = \frac{7}{26} \sqrt{13} \text{.}\) 1p |
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BreukInWortel (4)
008e - Wortels vereenvoudigen - basis - 1ms
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Getal & Ruimte (12e editie) - havo wiskunde B - 3.3 Getal & Ruimte (13e editie) - 3 vwo - 5.5 Getal & Ruimte (13e editie) - havo wiskunde B - 7.2 |
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Herleid. 1p \(\sqrt{9\frac{3}{8}}\) |
○ \(\sqrt{9\frac{3}{8}} = \sqrt{\frac{75}{8}} = {\sqrt{75} \over \sqrt{8}} ⋅ {\sqrt{8} \over \sqrt{8}} = {\sqrt{600} \over 8} = \frac{1}{8} \sqrt{600} = \frac{1}{8} ⋅ 10 ⋅ \sqrt{6} = 1\frac{1}{4} \sqrt{6} \text{.}\) 1p |
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Delen (4)
00dc - Wortels vereenvoudigen - basis - 9ms
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Getal & Ruimte (13e editie) - 2 havo/vwo - 5.3 Getal & Ruimte (13e editie) - 3 vwo - 5.5 |
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Herleid. 1p \({18 \sqrt{60} \over 3 \sqrt{5}}\) |
○ \({18 \sqrt{60} \over 3 \sqrt{5}} = {18 \over 3} ⋅ {\sqrt{60} \over \sqrt{5}} = 6 \sqrt{12} = 6 ⋅ \sqrt{4} ⋅ \sqrt{3} = 6 ⋅ 2 ⋅ \sqrt{3} = 12 \sqrt{3}\) 1p |
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FactorVoorWortelteken (1)
0086 - Wortels vereenvoudigen - basis - 0ms
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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 \(\sqrt{45}\) |
○ \(\sqrt{45} = \sqrt{9} ⋅ \sqrt{5} = 3 \sqrt{5} \text{.}\) 1p |
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FactorVoorWortelteken (2)
0087 - Wortels vereenvoudigen - basis - 0ms
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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 \(2 \sqrt{18}\) |
○ \(2 \sqrt{18} = 2 ⋅ \sqrt{9} ⋅ \sqrt{2} = 2 ⋅ 3 ⋅ \sqrt{2} = 6 \sqrt{2} \text{.}\) 1p |
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Optellen (5)
0085 - Wortels vereenvoudigen - basis - 0ms
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Getal & Ruimte (12e editie) - havo wiskunde B - 3.3 Getal & Ruimte (13e editie) - 2 vwo - 5.3 Getal & Ruimte (13e editie) - havo wiskunde B - 7.2 |
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Herleid. 2p \(\sqrt{48} + \sqrt{27}\) |
○ \(\sqrt{48} + \sqrt{27} = \sqrt{16} ⋅ \sqrt{3} + \sqrt{9} ⋅ \sqrt{3} = 4 \sqrt{3} + 3 \sqrt{3} \text{.}\) 1p ○ \(4 \sqrt{3} + 3 \sqrt{3} = 7 \sqrt{3} \text{.}\) 1p |
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Optellen (6)
0088 - Wortels vereenvoudigen - basis - 0ms
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Getal & Ruimte (12e editie) - havo wiskunde B - 3.3 Getal & Ruimte (13e editie) - 2 vwo - 5.3 Getal & Ruimte (13e editie) - havo wiskunde B - 7.2 |
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Herleid. 2p \(4 \sqrt{75} - 7 \sqrt{300}\) |
○ \(4 \sqrt{75} - 7 \sqrt{300} = 4 ⋅ \sqrt{25} ⋅ \sqrt{3} - 7 ⋅ \sqrt{100} ⋅ \sqrt{3} \text{.}\) 1p ○ \(4 ⋅ 5 ⋅ \sqrt{3} - 7 ⋅ 10 ⋅ \sqrt{3} = 20 \sqrt{3} - 70 \sqrt{3} = -50 \sqrt{3} \text{.}\) 1p |
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SomInNoemer (1)
00r3 - Wortels vereenvoudigen - basis - 1ms
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Getal & Ruimte (13e editie) - vwo wiskunde B - 3.3 |
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Herleid. 1p \({4 \over 1 + \sqrt{5}}\) |
○ \({4 \over 1 + \sqrt{5}} = {4 \over 1 + \sqrt{5}} ⋅ {1 - \sqrt{5} \over 1 - \sqrt{5}}\) 1p |
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SomInNoemer (2)
00r4 - Wortels vereenvoudigen - basis - 1ms
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Getal & Ruimte (13e editie) - vwo wiskunde B - 3.3 |
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Herleid. 1p \({3 \sqrt{6} \over \sqrt{2} - \sqrt{5}}\) |
○ \({3 \sqrt{6} \over \sqrt{2} - \sqrt{5}} = {3 \sqrt{6} \over \sqrt{2} - \sqrt{5}} ⋅ {\sqrt{2} + \sqrt{5} \over \sqrt{2} + \sqrt{5}}\) 1p |
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Vermenigvuldigen (5)
00dd - Wortels vereenvoudigen - basis - 3ms - data pool: #22 (2ms)
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Getal & Ruimte (13e editie) - 3 vwo - 5.5 Getal & Ruimte (13e editie) - havo wiskunde B - 7.2 |
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Herleid. 1p \(5 \sqrt{6} ⋅ 4 \sqrt{3}\) |
○ \(5 \sqrt{6} ⋅ 4 \sqrt{3} = 20 \sqrt{18} = 20 ⋅ \sqrt{9} ⋅ \sqrt{2} = 20 ⋅ 3 ⋅ \sqrt{2} = 60 \sqrt{2}\) 1p |
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WortelInNoemer
0089 - Wortels vereenvoudigen - basis - 1ms
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Getal & Ruimte (12e editie) - havo wiskunde B - 3.3 Getal & Ruimte (13e editie) - 3 vwo - 5.5 Getal & Ruimte (13e editie) - havo wiskunde B - 7.2 |
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Herleid. 1p \({4 \over 7 \sqrt{7}}\) |
○ \({4 \over 7 \sqrt{7}} = {4 \over 7 \sqrt{7}} ⋅ {\sqrt{7} \over \sqrt{7}} = {4 \sqrt{7} \over 7 ⋅ 7} = \frac{4}{49} \sqrt{7} \text{.}\) 1p |