Getal & Ruimte (13e editie) - 2 havo/vwo

'Wortels vereenvoudigen'.

2 havo/vwo 5.3 Wortels herleiden

Wortels vereenvoudigen (4)

opgave 1

Herleid.

1p

a

\(\sqrt{28}\)

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

a

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

1p

1p

b

\(-3 \sqrt{112}\)

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

b

\(-3 \sqrt{112} = -3 ⋅ \sqrt{16} ⋅ \sqrt{7} = -3 ⋅ 4 ⋅ \sqrt{7} = -12 \sqrt{7} \text{.}\)

1p

1p

c

\(\sqrt{\frac{16}{49}}\)

BreukInWortel (1)
008b - Wortels vereenvoudigen - basis - 25ms

c

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

1p

1p

d

\({45 \sqrt{400} \over 5 \sqrt{10}}\)

Delen (4)
00dc - Wortels vereenvoudigen - basis - 1ms

d

\({45 \sqrt{400} \over 5 \sqrt{10}} = {45 \over 5} ⋅ {\sqrt{400} \over \sqrt{10}} = 9 \sqrt{40} = 9 ⋅ \sqrt{4} ⋅ \sqrt{10} = 9 ⋅ 2 ⋅ \sqrt{10} = 18 \sqrt{10}\)

1p

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