Getal & Ruimte (13e editie) - 3 havo
'Wortels vereenvoudigen'.
| 2 havo/vwo | 5.3 Wortels herleiden |
opgave 1Herleid. 1p a \(\sqrt{175}\) FactorVoorWortelteken (1) 0086 - Wortels vereenvoudigen - basis - 0ms a \(\sqrt{175} = \sqrt{25} ⋅ \sqrt{7} = 5 \sqrt{7} \text{.}\) 1p 1p b \(-6 \sqrt{27}\) FactorVoorWortelteken (2) 0087 - Wortels vereenvoudigen - basis - 0ms b \(-6 \sqrt{27} = -6 ⋅ \sqrt{9} ⋅ \sqrt{3} = -6 ⋅ 3 ⋅ \sqrt{3} = -18 \sqrt{3} \text{.}\) 1p 1p c \(\sqrt{2\frac{1}{4}}\) BreukInWortel (1) 008b - Wortels vereenvoudigen - basis - 72ms c \(\sqrt{2\frac{1}{4}} = \sqrt{\frac{9}{4}} = {\sqrt{9} \over \sqrt{4}} = \frac{3}{2} = 1\frac{1}{2} \text{.}\) 1p 1p d \({24 \sqrt{400} \over 8 \sqrt{10}}\) Delen (4) 00dc - Wortels vereenvoudigen - basis - 7ms d \({24 \sqrt{400} \over 8 \sqrt{10}} = {24 \over 8} ⋅ {\sqrt{400} \over \sqrt{10}} = 3 \sqrt{40} = 3 ⋅ \sqrt{4} ⋅ \sqrt{10} = 3 ⋅ 2 ⋅ \sqrt{10} = 6 \sqrt{10}\) 1p |
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| 3 havo | 5.4 Wortels herleiden |
opgave 1Herleid. 1p \(\sqrt{1\frac{4}{9}}\) BreukInWortel (2) 008c - Wortels vereenvoudigen - basis - 1ms ○ \(\sqrt{1\frac{4}{9}} = \sqrt{\frac{13}{9}} = {\sqrt{13} \over \sqrt{9}} = {\sqrt{13} \over 3} = \frac{1}{3} \sqrt{13} \text{.}\) 1p |