Getal & Ruimte (13e editie) - 2 vwo

'Wortels vereenvoudigen'.

2 vwo 5.3 Wortels herleiden

Wortels vereenvoudigen (5)

opgave 1

Herleid.

2p

a

\(\sqrt{80}+\sqrt{500}\)

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

a

\(\sqrt{80}+\sqrt{500}=\sqrt{16}⋅\sqrt{5}+\sqrt{100}⋅\sqrt{5}=4\sqrt{5}+10\sqrt{5}\text{.}\)

1p

\(4\sqrt{5}+10\sqrt{5}=14\sqrt{5}\text{.}\)

1p

1p

b

\(\sqrt{20}\)

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

b

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

1p

1p

c

\(7\sqrt{28}\)

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

c

\(7\sqrt{28}=7⋅\sqrt{4}⋅\sqrt{7}=7⋅2⋅\sqrt{7}=14\sqrt{7}\text{.}\)

1p

2p

d

\(2\sqrt{200}-3\sqrt{32}\)

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

d

\(2\sqrt{200}-3\sqrt{32}=2⋅\sqrt{100}⋅\sqrt{2}-3⋅\sqrt{16}⋅\sqrt{2}\text{.}\)

1p

\(2⋅10⋅\sqrt{2}-3⋅4⋅\sqrt{2}=20\sqrt{2}-12\sqrt{2}=8\sqrt{2}\text{.}\)

1p

opgave 2

Herleid.

1p

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

BreukInWortel (1)
008b - Wortels vereenvoudigen - basis - 68ms

\(\sqrt{\frac{1}{25}}={\sqrt{1} \over \sqrt{25}}=\frac{1}{5}\text{.}\)

1p

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