What is 3sqrt((-2)^3) ?

The solution to 3sqrt((-2)^3) is 6sqrt(2)i

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simplify 3sqrt((-2)^3)

simplify

3 (- 2)^{3}

62 i

Solution steps

3 (- 2)^{3}

(- 2)^{3} = - 8

= 3 - 8

Prime factorization of

8 : 2^{3}

= 3 - 2^{3}

Apply exponent rule:

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

- 2^{3} = - 2^{2} \cdot 2

= 3 - 2^{2} \cdot 2

Apply radical rule:

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

- 2^{2} \cdot 2 = 2^{2} - 2

= 3 2^{2} - 2

Apply radical rule:

a^{2} = a, a \geq 0

2^{2} = 2

= 3 \cdot 2 - 2

Apply radical rule:

- a = a - 1

- 2 = 2 - 1

= 3 \cdot 22 - 1

Apply imaginary number rule:

- 1 = i

= 3 \cdot 22 i

Multiply the numbers:

3 \cdot 2 = 6

= 62 i

(8 v)^{2}

2 x^{2} + 162

2 x^{2} + 200

\frac{9 + 8 - 1}{2}

\frac{5}{10} + \frac{1}{5}