Getal & Ruimte (13e editie) - 2 vwo

'Wortels vereenvoudigen'.

2 vwo 5.3 Wortels herleiden

Wortels vereenvoudigen (5)

opgave 1

Herleid.

2p

a

\(\sqrt{18}+\sqrt{32}\)

Optellen (5)
0085 - Wortels vereenvoudigen - basis - 0ms

a

\(\sqrt{18}+\sqrt{32}=\sqrt{9}⋅\sqrt{2}+\sqrt{16}⋅\sqrt{2}=3\sqrt{2}+4\sqrt{2}\text{.}\)

1p

○

\(3\sqrt{2}+4\sqrt{2}=7\sqrt{2}\text{.}\)

1p

1p

b

\(\sqrt{27}\)

FactorVoorWortelteken (1)
0086 - Wortels vereenvoudigen - basis - 0ms

b

\(\sqrt{27}=\sqrt{9}⋅\sqrt{3}=3\sqrt{3}\text{.}\)

1p

1p

c

\(-7\sqrt{300}\)

FactorVoorWortelteken (2)
0087 - Wortels vereenvoudigen - basis - 0ms

c

\(-7\sqrt{300}=-7⋅\sqrt{100}⋅\sqrt{3}=-7⋅10⋅\sqrt{3}=-70\sqrt{3}\text{.}\)

1p

2p

d

\(2\sqrt{75}-3\sqrt{27}\)

Optellen (6)
0088 - Wortels vereenvoudigen - basis - 0ms

d

\(2\sqrt{75}-3\sqrt{27}=2⋅\sqrt{25}⋅\sqrt{3}-3⋅\sqrt{9}⋅\sqrt{3}\text{.}\)

1p

○

\(2⋅5⋅\sqrt{3}-3⋅3⋅\sqrt{3}=10\sqrt{3}-9\sqrt{3}=1\sqrt{3}\text{.}\)

1p

opgave 2

Herleid.

1p

\(\sqrt{3\frac{1}{16}}\)

BreukInWortel (1)
008b - Wortels vereenvoudigen - basis - 56ms

○

\(\sqrt{3\frac{1}{16}}=\sqrt{\frac{49}{16}}={\sqrt{49} \over \sqrt{16}}=\frac{7}{4}=1\frac{3}{4}\text{.}\)

1p
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