Getal & Ruimte (12e editie) - havo wiskunde A
'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 \(-2 \sqrt{50}\) FactorVoorWortelteken (2) 0087 - Wortels vereenvoudigen - basis - 0ms b \(-2 \sqrt{50} = -2 ⋅ \sqrt{25} ⋅ \sqrt{2} = -2 ⋅ 5 ⋅ \sqrt{2} = -10 \sqrt{2} \text{.}\) 1p 1p c \(\sqrt{\frac{49}{100}}\) BreukInWortel (1) 008b - Wortels vereenvoudigen - basis - 31ms c \(\sqrt{\frac{49}{100}} = {\sqrt{49} \over \sqrt{100}} = \frac{7}{10} \text{.}\) 1p 1p d \({32 \sqrt{72} \over 8 \sqrt{3}}\) Delen (4) 00dc - Wortels vereenvoudigen - basis - 1ms d \({32 \sqrt{72} \over 8 \sqrt{3}} = {32 \over 8} ⋅ {\sqrt{72} \over \sqrt{3}} = 4 \sqrt{24} = 4 ⋅ \sqrt{4} ⋅ \sqrt{6} = 4 ⋅ 2 ⋅ \sqrt{6} = 8 \sqrt{6}\) 1p |
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| 3 havo | 5.4 Wortels herleiden |
opgave 1Herleid. 1p \(\sqrt{3\frac{17}{25}}\) BreukInWortel (2) 008c - Wortels vereenvoudigen - basis - 1ms ○ \(\sqrt{3\frac{17}{25}} = \sqrt{\frac{92}{25}} = {\sqrt{92} \over \sqrt{25}} = {\sqrt{92} \over 5} = \frac{1}{5} \sqrt{92} = \frac{1}{5} ⋅ 2 ⋅ \sqrt{23} = \frac{2}{5} \sqrt{23} \text{.}\) 1p |