Getal & Ruimte (13e editie) - 3 havo
'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 \(-6 \sqrt{32}\) FactorVoorWortelteken (2) 0087 - Wortels vereenvoudigen - basis - 0ms b \(-6 \sqrt{32} = -6 ⋅ \sqrt{16} ⋅ \sqrt{2} = -6 ⋅ 4 ⋅ \sqrt{2} = -24 \sqrt{2} \text{.}\) 1p 1p c \(\sqrt{\frac{49}{81}}\) BreukInWortel (1) 008b - Wortels vereenvoudigen - basis - 72ms c \(\sqrt{\frac{49}{81}} = {\sqrt{49} \over \sqrt{81}} = \frac{7}{9} \text{.}\) 1p 1p d \({42 \sqrt{160} \over 7 \sqrt{8}}\) Delen (4) 00dc - Wortels vereenvoudigen - basis - 7ms d \({42 \sqrt{160} \over 7 \sqrt{8}} = {42 \over 7} ⋅ {\sqrt{160} \over \sqrt{8}} = 6 \sqrt{20} = 6 ⋅ \sqrt{4} ⋅ \sqrt{5} = 6 ⋅ 2 ⋅ \sqrt{5} = 12 \sqrt{5}\) 1p |
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| 3 havo | 5.4 Wortels herleiden |
opgave 1Herleid. 1p \(\sqrt{1\frac{39}{49}}\) BreukInWortel (2) 008c - Wortels vereenvoudigen - basis - 1ms ○ \(\sqrt{1\frac{39}{49}} = \sqrt{\frac{88}{49}} = {\sqrt{88} \over \sqrt{49}} = {\sqrt{88} \over 7} = \frac{1}{7} \sqrt{88} = \frac{1}{7} ⋅ 2 ⋅ \sqrt{22} = \frac{2}{7} \sqrt{22} \text{.}\) 1p |