Getal & Ruimte (13e editie) - 2 vwo

'Wortels vereenvoudigen'.

2 vwo 5.3 Wortels herleiden

Wortels vereenvoudigen (5)

opgave 1

Herleid.

2p

a

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

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

a

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

1p

○

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

1p

1p

b

\(\sqrt{75}\)

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

b

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

1p

1p

c

\(-5\sqrt{125}\)

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

c

\(-5\sqrt{125}=-5⋅\sqrt{25}⋅\sqrt{5}=-5⋅5⋅\sqrt{5}=-25\sqrt{5}\text{.}\)

1p

2p

d

\(4\sqrt{48}-7\sqrt{27}\)

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

d

\(4\sqrt{48}-7\sqrt{27}=4⋅\sqrt{16}⋅\sqrt{3}-7⋅\sqrt{9}⋅\sqrt{3}\text{.}\)

1p

○

\(4⋅4⋅\sqrt{3}-7⋅3⋅\sqrt{3}=16\sqrt{3}-21\sqrt{3}=-5\sqrt{3}\text{.}\)

1p

opgave 2

Herleid.

1p

\(\sqrt{6\frac{1}{4}}\)

BreukInWortel (1)
008b - Wortels vereenvoudigen - basis - 0ms

○

\(\sqrt{6\frac{1}{4}}=\sqrt{\frac{25}{4}}={\sqrt{25} \over \sqrt{4}}=\frac{5}{2}=2\frac{1}{2}\text{.}\)

1p
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