The solution to 3sqrt(-27) is 9sqrt(3)i

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simplify 3sqrt(-27)

Solution

simplify

3 - 27

93 i

Solution steps

3 - 27

Prime factorization of

27 : 3^{3}

= 3 - 3^{3}

Apply exponent rule:

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

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

= 3 - 3^{2} \cdot 3

Apply radical rule:

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

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

= 3 3^{2} - 3

Apply radical rule:

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

3^{2} = 3

= 3 \cdot 3 - 3

Multiply the numbers:

3 \cdot 3 = 9

= 9 - 3

Apply radical rule:

- a = a - 1

- 3 = 3 - 1

= 93 - 1

Apply imaginary number rule:

- 1 = i

= 93 i

\frac{3 x - 1}{x - 2} \leq 4

7^{2} + 5^{2}

4 + 42

\frac{w}{- 6} = 8

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