Getal & Ruimte (13e editie) - 2 vwo
'Wortels vereenvoudigen'.
| 2 vwo | 5.3 Wortels herleiden |
opgave 1Herleid. 2p a \(\sqrt{45}+\sqrt{125}\) Optellen (5) 0085 - Wortels vereenvoudigen - basis - 0ms a \(\sqrt{45}+\sqrt{125}=\sqrt{9}⋅\sqrt{5}+\sqrt{25}⋅\sqrt{5}=3\sqrt{5}+5\sqrt{5}\text{.}\) 1p ○ \(3\sqrt{5}+5\sqrt{5}=8\sqrt{5}\text{.}\) 1p 1p b \(\sqrt{18}\) FactorVoorWortelteken (1) 0086 - Wortels vereenvoudigen - basis - 0ms b \(\sqrt{18}=\sqrt{9}⋅\sqrt{2}=3\sqrt{2}\text{.}\) 1p 1p c \(-3\sqrt{28}\) FactorVoorWortelteken (2) 0087 - Wortels vereenvoudigen - basis - 0ms c \(-3\sqrt{28}=-3⋅\sqrt{4}⋅\sqrt{7}=-3⋅2⋅\sqrt{7}=-6\sqrt{7}\text{.}\) 1p 2p d \(3\sqrt{45}-2\sqrt{125}\) Optellen (6) 0088 - Wortels vereenvoudigen - basis - 1ms d \(3\sqrt{45}-2\sqrt{125}=3⋅\sqrt{9}⋅\sqrt{5}-2⋅\sqrt{25}⋅\sqrt{5}\text{.}\) 1p ○ \(3⋅3⋅\sqrt{5}-2⋅5⋅\sqrt{5}=9\sqrt{5}-10\sqrt{5}=-1\sqrt{5}\text{.}\) 1p opgave 2Herleid. 1p \(\sqrt{\frac{16}{81}}\) BreukInWortel (1) 008b - Wortels vereenvoudigen - basis - 68ms ○ \(\sqrt{\frac{16}{81}}={\sqrt{16} \over \sqrt{81}}=\frac{4}{9}\text{.}\) 1p |