Wortels vereenvoudigen
2i - 13 oefeningen
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BreukInWortel (1)
008b - Wortels vereenvoudigen - basis - 72ms
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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 \(\sqrt{1\frac{24}{25}}\) |
○ \(\sqrt{1\frac{24}{25}} = \sqrt{\frac{49}{25}} = {\sqrt{49} \over \sqrt{25}} = \frac{7}{5} = 1\frac{2}{5} \text{.}\) 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 \(\sqrt{3\frac{9}{25}}\) |
○ \(\sqrt{3\frac{9}{25}} = \sqrt{\frac{84}{25}} = {\sqrt{84} \over \sqrt{25}} = {\sqrt{84} \over 5} = \frac{1}{5} \sqrt{84} = \frac{1}{5} ⋅ 2 ⋅ \sqrt{21} = \frac{2}{5} \sqrt{21} \text{.}\) 1p |
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BreukInWortel (3)
008d - Wortels vereenvoudigen - basis - 0ms
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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 \(\sqrt{\frac{1}{57}}\) |
○ \(\sqrt{\frac{1}{57}} = {\sqrt{1} \over \sqrt{57}} = {1 \over \sqrt{57}} ⋅ {\sqrt{57} \over \sqrt{57}} = {\sqrt{57} \over 57} = \frac{1}{57} \sqrt{57} \text{.}\) 1p |
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BreukInWortel (4)
008e - Wortels vereenvoudigen - basis - 0ms
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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 \(\sqrt{\frac{2}{27}}\) |
○ \(\sqrt{\frac{2}{27}} = {\sqrt{2} \over \sqrt{27}} ⋅ {\sqrt{27} \over \sqrt{27}} = {\sqrt{54} \over 27} = \frac{1}{27} \sqrt{54} = \frac{1}{27} ⋅ 3 ⋅ \sqrt{6} = \frac{1}{9} \sqrt{6} \text{.}\) 1p |
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Delen (4)
00dc - Wortels vereenvoudigen - basis - 7ms
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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 \({30 \sqrt{48} \over 5 \sqrt{6}}\) |
○ \({30 \sqrt{48} \over 5 \sqrt{6}} = {30 \over 5} ⋅ {\sqrt{48} \over \sqrt{6}} = 6 \sqrt{8} = 6 ⋅ \sqrt{4} ⋅ \sqrt{2} = 6 ⋅ 2 ⋅ \sqrt{2} = 12 \sqrt{2}\) 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 \(\sqrt{27}\) |
○ \(\sqrt{27} = \sqrt{9} ⋅ \sqrt{3} = 3 \sqrt{3} \text{.}\) 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 \(-7 \sqrt{48}\) |
○ \(-7 \sqrt{48} = -7 ⋅ \sqrt{16} ⋅ \sqrt{3} = -7 ⋅ 4 ⋅ \sqrt{3} = -28 \sqrt{3} \text{.}\) 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 \(\sqrt{27} + \sqrt{12}\) |
○ \(\sqrt{27} + \sqrt{12} = \sqrt{9} ⋅ \sqrt{3} + \sqrt{4} ⋅ \sqrt{3} = 3 \sqrt{3} + 2 \sqrt{3} \text{.}\) 1p ○ \(3 \sqrt{3} + 2 \sqrt{3} = 5 \sqrt{3} \text{.}\) 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 \(6 \sqrt{20} + 3 \sqrt{500}\) |
○ \(6 \sqrt{20} + 3 \sqrt{500} = 6 ⋅ \sqrt{4} ⋅ \sqrt{5} + 3 ⋅ \sqrt{100} ⋅ \sqrt{5} \text{.}\) 1p ○ \(6 ⋅ 2 ⋅ \sqrt{5} + 3 ⋅ 10 ⋅ \sqrt{5} = 12 \sqrt{5} + 30 \sqrt{5} = 42 \sqrt{5} \text{.}\) 1p |
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SomInNoemer (1)
00r3 - Wortels vereenvoudigen - basis - 0ms
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Getal & Ruimte (13e editie) - vwo wiskunde B - 3.3 |
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Herleid. 1p \({-5 \over 6 - \sqrt{2}}\) |
○ \({-5 \over 6 - \sqrt{2}} = {-5 \over 6 - \sqrt{2}} ⋅ {6 + \sqrt{2} \over 6 + \sqrt{2}}\) 1p |
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SomInNoemer (2)
00r4 - Wortels vereenvoudigen - basis - 0ms
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Getal & Ruimte (13e editie) - vwo wiskunde B - 3.3 |
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Herleid. 1p \({6 \sqrt{5} \over \sqrt{3} + \sqrt{2}}\) |
○ \({6 \sqrt{5} \over \sqrt{3} + \sqrt{2}} = {6 \sqrt{5} \over \sqrt{3} + \sqrt{2}} ⋅ {\sqrt{3} - \sqrt{2} \over \sqrt{3} - \sqrt{2}}\) 1p |
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Vermenigvuldigen (5)
00dd - Wortels vereenvoudigen - basis - 2ms - 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 \(2 \sqrt{6} ⋅ 4 \sqrt{10}\) |
○ \(2 \sqrt{6} ⋅ 4 \sqrt{10} = 8 \sqrt{60} = 8 ⋅ \sqrt{4} ⋅ \sqrt{15} = 8 ⋅ 2 ⋅ \sqrt{15} = 16 \sqrt{15}\) 1p |
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WortelInNoemer
0089 - Wortels vereenvoudigen - basis - 0ms
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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 \({3 \over 4 \sqrt{5}}\) |
○ \({3 \over 4 \sqrt{5}} = {3 \over 4 \sqrt{5}} ⋅ {\sqrt{5} \over \sqrt{5}} = {3 \sqrt{5} \over 4 ⋅ 5} = \frac{3}{20} \sqrt{5} \text{.}\) 1p |