Getal & Ruimte (12e editie) - havo wiskunde A

'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

\(-2 \sqrt{50}\)

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

b

\(-2 \sqrt{50} = -2 ⋅ \sqrt{25} ⋅ \sqrt{2} = -2 ⋅ 5 ⋅ \sqrt{2} = -10 \sqrt{2} \text{.}\)

1p

1p

c

\(\sqrt{\frac{49}{100}}\)

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

c

\(\sqrt{\frac{49}{100}} = {\sqrt{49} \over \sqrt{100}} = \frac{7}{10} \text{.}\)

1p

1p

d

\({32 \sqrt{72} \over 8 \sqrt{3}}\)

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

d

\({32 \sqrt{72} \over 8 \sqrt{3}} = {32 \over 8} ⋅ {\sqrt{72} \over \sqrt{3}} = 4 \sqrt{24} = 4 ⋅ \sqrt{4} ⋅ \sqrt{6} = 4 ⋅ 2 ⋅ \sqrt{6} = 8 \sqrt{6}\)

1p

3 havo 5.4 Wortels herleiden

Wortels vereenvoudigen (1)

opgave 1

Herleid.

1p

\(\sqrt{3\frac{17}{25}}\)

BreukInWortel (2)
008c - Wortels vereenvoudigen - basis - 1ms

○

\(\sqrt{3\frac{17}{25}} = \sqrt{\frac{92}{25}} = {\sqrt{92} \over \sqrt{25}} = {\sqrt{92} \over 5} = \frac{1}{5} \sqrt{92} = \frac{1}{5} ⋅ 2 ⋅ \sqrt{23} = \frac{2}{5} \sqrt{23} \text{.}\)

1p

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