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

'Wortels vereenvoudigen'.

2 havo/vwo 5.3 Wortels herleiden

Wortels vereenvoudigen (4)

opgave 1

Herleid.

1p

a

\(\sqrt{20}\)

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

a

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

1p

1p

b

\(-3 \sqrt{8}\)

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

b

\(-3 \sqrt{8} = -3 ⋅ \sqrt{4} ⋅ \sqrt{2} = -3 ⋅ 2 ⋅ \sqrt{2} = -6 \sqrt{2} \text{.}\)

1p

1p

c

\(\sqrt{2\frac{14}{25}}\)

BreukInWortel (1)
008b - Wortels vereenvoudigen - basis - 31ms

c

\(\sqrt{2\frac{14}{25}} = \sqrt{\frac{64}{25}} = {\sqrt{64} \over \sqrt{25}} = \frac{8}{5} = 1\frac{3}{5} \text{.}\)

1p

1p

d

\({18 \sqrt{140} \over 9 \sqrt{7}}\)

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

d

\({18 \sqrt{140} \over 9 \sqrt{7}} = {18 \over 9} ⋅ {\sqrt{140} \over \sqrt{7}} = 2 \sqrt{20} = 2 ⋅ \sqrt{4} ⋅ \sqrt{5} = 2 ⋅ 2 ⋅ \sqrt{5} = 4 \sqrt{5}\)

1p

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