vereinfachen \sqrt[3]{2sqrt(2)}

Lösung

vereinfachen

322

2

Dezimale

1.41421 \dots

Schritte zur Lösung

322

Wende Radikal Regel an:

n ab = n a n b, a \geq 0, b \geq 0

322 = 3232

= 3232

32 = 62

= 3262

Wende Radikal Regel an:

n a = a^{\frac{1}{n}}

32 = 2^{\frac{1}{3}}

= 2^{\frac{1}{3}} 62

Wende Radikal Regel an:

n a = a^{\frac{1}{n}}

62 = 2^{\frac{1}{6}}

= 2^{\frac{1}{3}} \cdot 2^{\frac{1}{6}}

Wende Exponentenregel an:

a^{b} \cdot a^{c} = a^{b + c}

2^{\frac{1}{3}} \cdot 2^{\frac{1}{6}} = 2^{\frac{1}{3} + \frac{1}{6}}

= 2^{\frac{1}{3} + \frac{1}{6}}

\frac{1}{3} + \frac{1}{6} = \frac{1}{2}

= 2^{\frac{1}{2}}

Wende Exponentenregel an:

a^{\frac{1}{2}} = a

2^{\frac{1}{2}} = 2

= 2

f a c t or x^{3} + y^{3}

\frac{x + 4}{2} = 5

s im pl i f y - (\frac{1}{3})^{2}

\frac{4 - x}{2} + 3 x = \frac{1}{2}

(3 x + 2)^{2} = 9