Wortels vereenvoudigen
2i - 13 oefeningen
|
BreukInWortel (1)
008b - Wortels vereenvoudigen - basis - 72ms
|
Getal & Ruimte (13e editie) - 2 havo/vwo - 5.3 Getal & Ruimte (13e editie) - 2 vwo - 5.3 |
|
Herleid. 1p \(\sqrt{\frac{9}{49}}\) |
○ \(\sqrt{\frac{9}{49}} = {\sqrt{9} \over \sqrt{49}} = \frac{3}{7} \text{.}\) 1p |
|
BreukInWortel (2)
008c - Wortels vereenvoudigen - basis - 1ms
|
Getal & Ruimte (13e editie) - 3 havo - 5.4 Getal & Ruimte (13e editie) - 3 vwo - 5.5 |
|
Herleid. 1p \(\sqrt{3\frac{4}{25}}\) |
○ \(\sqrt{3\frac{4}{25}} = \sqrt{\frac{79}{25}} = {\sqrt{79} \over \sqrt{25}} = {\sqrt{79} \over 5} = \frac{1}{5} \sqrt{79} \text{.}\) 1p |
|
BreukInWortel (3)
008d - Wortels vereenvoudigen - basis - 0ms
|
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 |
|
Herleid. 1p \(\sqrt{1\frac{13}{51}}\) |
○ \(\sqrt{1\frac{13}{51}} = \sqrt{\frac{64}{51}} = {\sqrt{64} \over \sqrt{51}} = {8 \over \sqrt{51}} ⋅ {\sqrt{51} \over \sqrt{51}} = {8 \sqrt{51} \over 51} = \frac{8}{51} \sqrt{51} \text{.}\) 1p |
|
BreukInWortel (4)
008e - Wortels vereenvoudigen - basis - 0ms
|
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 |
|
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 |
|
Delen (4)
00dc - Wortels vereenvoudigen - basis - 7ms
|
Getal & Ruimte (13e editie) - 2 havo/vwo - 5.3 Getal & Ruimte (13e editie) - 3 vwo - 5.5 |
|
Herleid. 1p \({24 \sqrt{120} \over 6 \sqrt{6}}\) |
○ \({24 \sqrt{120} \over 6 \sqrt{6}} = {24 \over 6} ⋅ {\sqrt{120} \over \sqrt{6}} = 4 \sqrt{20} = 4 ⋅ \sqrt{4} ⋅ \sqrt{5} = 4 ⋅ 2 ⋅ \sqrt{5} = 8 \sqrt{5}\) 1p |
|
FactorVoorWortelteken (1)
0086 - Wortels vereenvoudigen - basis - 0ms
|
Getal & Ruimte (13e editie) - 2 havo/vwo - 5.3 Getal & Ruimte (13e editie) - 2 vwo - 5.3 |
|
Herleid. 1p \(\sqrt{75}\) |
○ \(\sqrt{75} = \sqrt{25} ⋅ \sqrt{3} = 5 \sqrt{3} \text{.}\) 1p |
|
FactorVoorWortelteken (2)
0087 - Wortels vereenvoudigen - basis - 0ms
|
Getal & Ruimte (13e editie) - 2 havo/vwo - 5.3 Getal & Ruimte (13e editie) - 2 vwo - 5.3 |
|
Herleid. 1p \(5 \sqrt{8}\) |
○ \(5 \sqrt{8} = 5 ⋅ \sqrt{4} ⋅ \sqrt{2} = 5 ⋅ 2 ⋅ \sqrt{2} = 10 \sqrt{2} \text{.}\) 1p |
|
Optellen (5)
0085 - Wortels vereenvoudigen - basis - 0ms
|
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 |
|
Herleid. 2p \(\sqrt{500} + \sqrt{80}\) |
○ \(\sqrt{500} + \sqrt{80} = \sqrt{100} ⋅ \sqrt{5} + \sqrt{16} ⋅ \sqrt{5} = 10 \sqrt{5} + 4 \sqrt{5} \text{.}\) 1p ○ \(10 \sqrt{5} + 4 \sqrt{5} = 14 \sqrt{5} \text{.}\) 1p |
|
Optellen (6)
0088 - Wortels vereenvoudigen - basis - 0ms
|
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 |
|
Herleid. 2p \(3 \sqrt{12} + 7 \sqrt{27}\) |
○ \(3 \sqrt{12} + 7 \sqrt{27} = 3 ⋅ \sqrt{4} ⋅ \sqrt{3} + 7 ⋅ \sqrt{9} ⋅ \sqrt{3} \text{.}\) 1p ○ \(3 ⋅ 2 ⋅ \sqrt{3} + 7 ⋅ 3 ⋅ \sqrt{3} = 6 \sqrt{3} + 21 \sqrt{3} = 27 \sqrt{3} \text{.}\) 1p |
|
SomInNoemer (1)
00r3 - Wortels vereenvoudigen - basis - 0ms
|
Getal & Ruimte (13e editie) - vwo wiskunde B - 3.3 |
|
Herleid. 1p \({4 \over 6 + \sqrt{5}}\) |
○ \({4 \over 6 + \sqrt{5}} = {4 \over 6 + \sqrt{5}} ⋅ {6 - \sqrt{5} \over 6 - \sqrt{5}}\) 1p |
|
SomInNoemer (2)
00r4 - Wortels vereenvoudigen - basis - 0ms
|
Getal & Ruimte (13e editie) - vwo wiskunde B - 3.3 |
|
Herleid. 1p \({\sqrt{6} \over \sqrt{3} - \sqrt{5}}\) |
○ \({\sqrt{6} \over \sqrt{3} - \sqrt{5}} = {\sqrt{6} \over \sqrt{3} - \sqrt{5}} ⋅ {\sqrt{3} + \sqrt{5} \over \sqrt{3} + \sqrt{5}}\) 1p |
|
Vermenigvuldigen (5)
00dd - Wortels vereenvoudigen - basis - 2ms - data pool: #22 (2ms)
|
Getal & Ruimte (13e editie) - 3 vwo - 5.5 Getal & Ruimte (13e editie) - havo wiskunde B - 7.2 |
|
Herleid. 1p \(4 \sqrt{6} ⋅ 2 \sqrt{15}\) |
○ \(4 \sqrt{6} ⋅ 2 \sqrt{15} = 8 \sqrt{90} = 8 ⋅ \sqrt{9} ⋅ \sqrt{10} = 8 ⋅ 3 ⋅ \sqrt{10} = 24 \sqrt{10}\) 1p |
|
WortelInNoemer
0089 - Wortels vereenvoudigen - basis - 0ms
|
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 |
|
Herleid. 1p \({7 \over 6 \sqrt{7}}\) |
○ \({7 \over 6 \sqrt{7}} = {7 \over 6 \sqrt{7}} ⋅ {\sqrt{7} \over \sqrt{7}} = {7 \sqrt{7} \over 6 ⋅ 7} = \frac{1}{6} \sqrt{7} \text{.}\) 1p |