Getal & Ruimte (13e editie) - havo wiskunde B
'Wortels vereenvoudigen'.
| 2 havo/vwo | 5.3 Wortels herleiden |
opgave 1Herleid. 1p a \(\sqrt{28}\) FactorVoorWortelteken (1) 0086 - Wortels vereenvoudigen - basis - 0ms a \(\sqrt{28}=\sqrt{4}⋅\sqrt{7}=2\sqrt{7}\text{.}\) 1p 1p b \(5\sqrt{112}\) FactorVoorWortelteken (2) 0087 - Wortels vereenvoudigen - basis - 0ms b \(5\sqrt{112}=5⋅\sqrt{16}⋅\sqrt{7}=5⋅4⋅\sqrt{7}=20\sqrt{7}\text{.}\) 1p |
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| 3 havo | 5.4 Wortels herleiden |
opgave 1Herleid. 1p a \(\sqrt{1\frac{24}{25}}\) BreukInWortel (1) 008b - Wortels vereenvoudigen - basis - 0ms a \(\sqrt{1\frac{24}{25}}=\sqrt{\frac{49}{25}}={\sqrt{49} \over \sqrt{25}}=\frac{7}{5}=1\frac{2}{5}\text{.}\) 1p 1p b \(\sqrt{2\frac{4}{25}}\) BreukInWortel (2) 008c - Wortels vereenvoudigen - basis - 0ms b \(\sqrt{2\frac{4}{25}}=\sqrt{\frac{54}{25}}={\sqrt{54} \over \sqrt{25}}={\sqrt{54} \over 5}=\frac{1}{5}\sqrt{54}=\frac{1}{5}⋅3⋅\sqrt{6}=\frac{3}{5}\sqrt{6}\text{.}\) 1p |
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| havo wiskunde B | 7.2 Afstanden bij punten en lijnen |
opgave 1Herleid. 2p a \(\sqrt{20}+\sqrt{125}\) Optellen (5) 0085 - Wortels vereenvoudigen - basis - 0ms a \(\sqrt{20}+\sqrt{125}=\sqrt{4}⋅\sqrt{5}+\sqrt{25}⋅\sqrt{5}=2\sqrt{5}+5\sqrt{5}\text{.}\) 1p ○ \(2\sqrt{5}+5\sqrt{5}=7\sqrt{5}\text{.}\) 1p 2p b \(3\sqrt{50}-5\sqrt{32}\) Optellen (6) 0088 - Wortels vereenvoudigen - basis - 0ms b \(3\sqrt{50}-5\sqrt{32}=3⋅\sqrt{25}⋅\sqrt{2}-5⋅\sqrt{16}⋅\sqrt{2}\text{.}\) 1p ○ \(3⋅5⋅\sqrt{2}-5⋅4⋅\sqrt{2}=15\sqrt{2}-20\sqrt{2}=-5\sqrt{2}\text{.}\) 1p 1p c \({9 \over 5\sqrt{3}}\) WortelInNoemer 0089 - Wortels vereenvoudigen - basis - 0ms c \({9 \over 5\sqrt{3}}={9 \over 5\sqrt{3}}⋅{\sqrt{3} \over \sqrt{3}}={9\sqrt{3} \over 5⋅3}=\frac{3}{5}\sqrt{3}\text{.}\) 1p 1p d \(\sqrt{\frac{1}{50}}\) BreukInWortel (3) 008d - Wortels vereenvoudigen - basis - 1ms d \(\sqrt{\frac{1}{50}}={\sqrt{1} \over \sqrt{50}}={1 \over \sqrt{50}}⋅{\sqrt{50} \over \sqrt{50}}={\sqrt{50} \over 50}=\frac{1}{50}\sqrt{50}=\frac{1}{50}⋅5⋅\sqrt{2}=\frac{1}{10}\sqrt{2}\text{.}\) 1p opgave 2Herleid. 1p a \(\sqrt{\frac{2}{13}}\) BreukInWortel (4) 008e - Wortels vereenvoudigen - basis - 0ms a \(\sqrt{\frac{2}{13}}={\sqrt{2} \over \sqrt{13}}⋅{\sqrt{13} \over \sqrt{13}}={\sqrt{26} \over 13}=\frac{1}{13}\sqrt{26}\text{.}\) 1p 1p b \({40\sqrt{100} \over 5\sqrt{5}}\) Delen (4) 00dc - Wortels vereenvoudigen - basis - 10ms b \({40\sqrt{100} \over 5\sqrt{5}}={40 \over 5}⋅{\sqrt{100} \over \sqrt{5}}=8\sqrt{20}=8⋅\sqrt{4}⋅\sqrt{5}=8⋅2⋅\sqrt{5}=16\sqrt{5}\) 1p 1p c \(3\sqrt{6}⋅2\sqrt{3}\) Vermenigvuldigen (5) 00dd - Wortels vereenvoudigen - basis - 3ms - data pool: #22 (3ms) c \(3\sqrt{6}⋅2\sqrt{3}=6\sqrt{18}=6⋅\sqrt{9}⋅\sqrt{2}=6⋅3⋅\sqrt{2}=18\sqrt{2}\) 1p |