Getal & Ruimte (13e editie) - 2 havo/vwo
'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 \(-3 \sqrt{8}\) FactorVoorWortelteken (2) 0087 - Wortels vereenvoudigen - basis - 0ms b \(-3 \sqrt{8} = -3 ⋅ \sqrt{4} ⋅ \sqrt{2} = -3 ⋅ 2 ⋅ \sqrt{2} = -6 \sqrt{2} \text{.}\) 1p 1p c \(\sqrt{2\frac{14}{25}}\) BreukInWortel (1) 008b - Wortels vereenvoudigen - basis - 31ms c \(\sqrt{2\frac{14}{25}} = \sqrt{\frac{64}{25}} = {\sqrt{64} \over \sqrt{25}} = \frac{8}{5} = 1\frac{3}{5} \text{.}\) 1p 1p d \({18 \sqrt{140} \over 9 \sqrt{7}}\) Delen (4) 00dc - Wortels vereenvoudigen - basis - 1ms d \({18 \sqrt{140} \over 9 \sqrt{7}} = {18 \over 9} ⋅ {\sqrt{140} \over \sqrt{7}} = 2 \sqrt{20} = 2 ⋅ \sqrt{4} ⋅ \sqrt{5} = 2 ⋅ 2 ⋅ \sqrt{5} = 4 \sqrt{5}\) 1p |