The solution to 3sqrt(-24) is 6sqrt(6)i

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simplify 3sqrt(-24)

Solution

simplify

3 - 24

66 i

Solution steps

3 - 24

Prime factorization of

24 : 2^{3} \cdot 3

= 3 - 2^{3} \cdot 3

Apply exponent rule:

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

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

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

Apply radical rule:

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

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

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

Apply radical rule:

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

2^{2} = 2

= 3 \cdot 2 - 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 3 \cdot 2 - 6

Multiply the numbers:

3 \cdot 2 = 6

= 6 - 6

Apply radical rule:

- a = a - 1

- 6 = 6 - 1

= 66 - 1

Apply imaginary number rule:

- 1 = i

= 66 i

\frac{3}{1 + 2}

\frac{3 x ^{4} + 6 x}{2 x ^{4} + x ^{3} + 4 x + 2}

(- 2 + 2)^{e}

4 x^{2} - y^{2} - 2 x + y

\frac{2 i}{1 + 7 i}