The solution to 2sqrt(-27) is 6sqrt(3)i

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simplify 2sqrt(-27)

Solution

simplify

2 - 27

63 i

Solution steps

2 - 27

Prime factorization of

27 : 3^{3}

= 2 - 3^{3}

Apply exponent rule:

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

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

= 2 - 3^{2} \cdot 3

Apply radical rule:

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

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

= 2 3^{2} - 3

Apply radical rule:

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

3^{2} = 3

= 2 \cdot 3 - 3

Multiply the numbers:

2 \cdot 3 = 6

= 6 - 3

Apply radical rule:

- a = a - 1

- 3 = 3 - 1

= 63 - 1

Apply imaginary number rule:

- 1 = i

= 63 i

(q - 1) (q + 1)

12 \times 12 \times 12

\frac{2}{3} \times 12

(\frac{x}{20} + 1)^{20}

\frac{1}{2} \times \frac{1}{5}