Getal & Ruimte (13e editie) - havo wiskunde B
'Wortels vereenvoudigen'.
| 2 havo/vwo | 5.3 Wortels herleiden |
opgave 1Herleid. 1p a \(\sqrt{20}\) FactorVoorWortelteken (1) 0086 - Wortels vereenvoudigen - basis - 0ms a \(\sqrt{20}=\sqrt{4}⋅\sqrt{5}=2\sqrt{5}\text{.}\) 1p 1p b \(-2\sqrt{8}\) FactorVoorWortelteken (2) 0087 - Wortels vereenvoudigen - basis - 0ms b \(-2\sqrt{8}=-2⋅\sqrt{4}⋅\sqrt{2}=-2⋅2⋅\sqrt{2}=-4\sqrt{2}\text{.}\) 1p |
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| 3 havo | 5.4 Wortels herleiden |
opgave 1Herleid. 1p a \(\sqrt{\frac{25}{49}}\) BreukInWortel (1) 008b - Wortels vereenvoudigen - basis - 0ms a \(\sqrt{\frac{25}{49}}={\sqrt{25} \over \sqrt{49}}=\frac{5}{7}\text{.}\) 1p 1p b \(\sqrt{6\frac{1}{9}}\) BreukInWortel (2) 008c - Wortels vereenvoudigen - basis - 0ms b \(\sqrt{6\frac{1}{9}}=\sqrt{\frac{55}{9}}={\sqrt{55} \over \sqrt{9}}={\sqrt{55} \over 3}=\frac{1}{3}\sqrt{55}\text{.}\) 1p |
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| havo wiskunde B | 7.2 Afstanden bij punten en lijnen |
opgave 1Herleid. 2p a \(\sqrt{80}+\sqrt{20}\) Optellen (5) 0085 - Wortels vereenvoudigen - basis - 0ms a \(\sqrt{80}+\sqrt{20}=\sqrt{16}⋅\sqrt{5}+\sqrt{4}⋅\sqrt{5}=4\sqrt{5}+2\sqrt{5}\text{.}\) 1p ○ \(4\sqrt{5}+2\sqrt{5}=6\sqrt{5}\text{.}\) 1p 2p b \(4\sqrt{500}-7\sqrt{45}\) Optellen (6) 0088 - Wortels vereenvoudigen - basis - 0ms b \(4\sqrt{500}-7\sqrt{45}=4⋅\sqrt{100}⋅\sqrt{5}-7⋅\sqrt{9}⋅\sqrt{5}\text{.}\) 1p ○ \(4⋅10⋅\sqrt{5}-7⋅3⋅\sqrt{5}=40\sqrt{5}-21\sqrt{5}=19\sqrt{5}\text{.}\) 1p 1p c \({2 \over 3\sqrt{5}}\) WortelInNoemer 0089 - Wortels vereenvoudigen - basis - 0ms c \({2 \over 3\sqrt{5}}={2 \over 3\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={2\sqrt{5} \over 3⋅5}=\frac{2}{15}\sqrt{5}\text{.}\) 1p 1p d \(\sqrt{2\frac{2}{31}}\) BreukInWortel (3) 008d - Wortels vereenvoudigen - basis - 1ms d \(\sqrt{2\frac{2}{31}}=\sqrt{\frac{64}{31}}={\sqrt{64} \over \sqrt{31}}={8 \over \sqrt{31}}⋅{\sqrt{31} \over \sqrt{31}}={8\sqrt{31} \over 31}=\frac{8}{31}\sqrt{31}\text{.}\) 1p opgave 2Herleid. 1p a \(\sqrt{4\frac{2}{3}}\) BreukInWortel (4) 008e - Wortels vereenvoudigen - basis - 0ms a \(\sqrt{4\frac{2}{3}}=\sqrt{\frac{14}{3}}={\sqrt{14} \over \sqrt{3}}⋅{\sqrt{3} \over \sqrt{3}}={\sqrt{42} \over 3}=\frac{1}{3}\sqrt{42}\text{.}\) 1p 1p b \({20\sqrt{56} \over 5\sqrt{2}}\) Delen (4) 00dc - Wortels vereenvoudigen - basis - 10ms b \({20\sqrt{56} \over 5\sqrt{2}}={20 \over 5}⋅{\sqrt{56} \over \sqrt{2}}=4\sqrt{28}=4⋅\sqrt{4}⋅\sqrt{7}=4⋅2⋅\sqrt{7}=8\sqrt{7}\) 1p 1p c \(3\sqrt{15}⋅4\sqrt{6}\) Vermenigvuldigen (5) 00dd - Wortels vereenvoudigen - basis - 3ms - data pool: #22 (3ms) c \(3\sqrt{15}⋅4\sqrt{6}=12\sqrt{90}=12⋅\sqrt{9}⋅\sqrt{10}=12⋅3⋅\sqrt{10}=36\sqrt{10}\) 1p |