Getal & Ruimte (13e editie) - 2 havo/vwo
'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 \(-3 \sqrt{112}\) FactorVoorWortelteken (2) 0087 - Wortels vereenvoudigen - basis - 0ms b \(-3 \sqrt{112} = -3 ⋅ \sqrt{16} ⋅ \sqrt{7} = -3 ⋅ 4 ⋅ \sqrt{7} = -12 \sqrt{7} \text{.}\) 1p 1p c \(\sqrt{\frac{16}{49}}\) BreukInWortel (1) 008b - Wortels vereenvoudigen - basis - 25ms c \(\sqrt{\frac{16}{49}} = {\sqrt{16} \over \sqrt{49}} = \frac{4}{7} \text{.}\) 1p 1p d \({45 \sqrt{400} \over 5 \sqrt{10}}\) Delen (4) 00dc - Wortels vereenvoudigen - basis - 1ms d \({45 \sqrt{400} \over 5 \sqrt{10}} = {45 \over 5} ⋅ {\sqrt{400} \over \sqrt{10}} = 9 \sqrt{40} = 9 ⋅ \sqrt{4} ⋅ \sqrt{10} = 9 ⋅ 2 ⋅ \sqrt{10} = 18 \sqrt{10}\) 1p |