Getal & Ruimte (13e editie) - 2 vwo

'Wortels vereenvoudigen'.

2 vwo 5.3 Wortels herleiden

Wortels vereenvoudigen (5)

opgave 1

Herleid.

2p

a

\(\sqrt{75} + \sqrt{300}\)

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

a

\(\sqrt{75} + \sqrt{300} = \sqrt{25} ⋅ \sqrt{3} + \sqrt{100} ⋅ \sqrt{3} = 5 \sqrt{3} + 10 \sqrt{3} \text{.}\)

1p

○

\(5 \sqrt{3} + 10 \sqrt{3} = 15 \sqrt{3} \text{.}\)

1p

1p

b

\(\sqrt{48}\)

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

b

\(\sqrt{48} = \sqrt{16} ⋅ \sqrt{3} = 4 \sqrt{3} \text{.}\)

1p

1p

c

\(3 \sqrt{300}\)

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

c

\(3 \sqrt{300} = 3 ⋅ \sqrt{100} ⋅ \sqrt{3} = 3 ⋅ 10 ⋅ \sqrt{3} = 30 \sqrt{3} \text{.}\)

1p

2p

d

\(5 \sqrt{75} + 3 \sqrt{300}\)

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

d

\(5 \sqrt{75} + 3 \sqrt{300} = 5 ⋅ \sqrt{25} ⋅ \sqrt{3} + 3 ⋅ \sqrt{100} ⋅ \sqrt{3} \text{.}\)

1p

○

\(5 ⋅ 5 ⋅ \sqrt{3} + 3 ⋅ 10 ⋅ \sqrt{3} = 25 \sqrt{3} + 30 \sqrt{3} = 55 \sqrt{3} \text{.}\)

1p

opgave 2

Herleid.

1p

\(\sqrt{1\frac{19}{81}}\)

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

○

\(\sqrt{1\frac{19}{81}} = \sqrt{\frac{100}{81}} = {\sqrt{100} \over \sqrt{81}} = \frac{10}{9} = 1\frac{1}{9} \text{.}\)

1p
"