Getal & Ruimte (13e editie) - 2 vwo

'Wortels vereenvoudigen'.

2 vwo 5.3 Wortels herleiden

Wortels vereenvoudigen (5)

opgave 1

Herleid.

2p

a

\(\sqrt{27}+\sqrt{75}\)

Optellen (5)
0085 - Wortels vereenvoudigen - basis - 1ms

a

\(\sqrt{27}+\sqrt{75}=\sqrt{9}⋅\sqrt{3}+\sqrt{25}⋅\sqrt{3}=3\sqrt{3}+5\sqrt{3}\text{.}\)

1p

○

\(3\sqrt{3}+5\sqrt{3}=8\sqrt{3}\text{.}\)

1p

1p

b

\(\sqrt{300}\)

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

b

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

1p

1p

c

\(-5\sqrt{12}\)

FactorVoorWortelteken (2)
0087 - Wortels vereenvoudigen - basis - 1ms

c

\(-5\sqrt{12}=-5⋅\sqrt{4}⋅\sqrt{3}=-5⋅2⋅\sqrt{3}=-10\sqrt{3}\text{.}\)

1p

2p

d

\(7\sqrt{27}+4\sqrt{12}\)

Optellen (6)
0088 - Wortels vereenvoudigen - basis - 1ms

d

\(7\sqrt{27}+4\sqrt{12}=7⋅\sqrt{9}⋅\sqrt{3}+4⋅\sqrt{4}⋅\sqrt{3}\text{.}\)

1p

○

\(7⋅3⋅\sqrt{3}+4⋅2⋅\sqrt{3}=21\sqrt{3}+8\sqrt{3}=29\sqrt{3}\text{.}\)

1p

opgave 2

Herleid.

1p

\(\sqrt{1\frac{24}{25}}\)

BreukInWortel (1)
008b - Wortels vereenvoudigen - basis - 103ms

○

\(\sqrt{1\frac{24}{25}}=\sqrt{\frac{49}{25}}={\sqrt{49} \over \sqrt{25}}=\frac{7}{5}=1\frac{2}{5}\text{.}\)

1p
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