Getal & Ruimte (13e editie) - 2 vwo

'Wortels vereenvoudigen'.

2 vwo 5.3 Wortels herleiden

Wortels vereenvoudigen (5)

opgave 1

Herleid.

2p

a

\(\sqrt{32}+\sqrt{8}\)

Optellen (5)
0085 - Wortels vereenvoudigen - basis

a

\(\sqrt{32}+\sqrt{8}=\sqrt{16}⋅\sqrt{2}+\sqrt{4}⋅\sqrt{2}=4\sqrt{2}+2\sqrt{2}\text{.}\)

1p

○

\(4\sqrt{2}+2\sqrt{2}=6\sqrt{2}\text{.}\)

1p

1p

b

\(\sqrt{500}\)

FactorVoorWortelteken (1)
0086 - Wortels vereenvoudigen - basis

b

\(\sqrt{500}=\sqrt{100}⋅\sqrt{5}=10\sqrt{5}\text{.}\)

1p

1p

c

\(4\sqrt{50}\)

FactorVoorWortelteken (2)
0087 - Wortels vereenvoudigen - basis

c

\(4\sqrt{50}=4⋅\sqrt{25}⋅\sqrt{2}=4⋅5⋅\sqrt{2}=20\sqrt{2}\text{.}\)

1p

2p

d

\(7\sqrt{75}+3\sqrt{300}\)

Optellen (6)
0088 - Wortels vereenvoudigen - basis

d

\(7\sqrt{75}+3\sqrt{300}=7⋅\sqrt{25}⋅\sqrt{3}+3⋅\sqrt{100}⋅\sqrt{3}\text{.}\)

1p

○

\(7⋅5⋅\sqrt{3}+3⋅10⋅\sqrt{3}=35\sqrt{3}+30\sqrt{3}=65\sqrt{3}\text{.}\)

1p

opgave 2

Herleid.

1p

\(\sqrt{\frac{1}{81}}\)

BreukInWortel (1)
008b - Wortels vereenvoudigen - basis

○

\(\sqrt{\frac{1}{81}}={\sqrt{1} \over \sqrt{81}}=\frac{1}{9}\text{.}\)

1p
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