What is simplify-3sqrt(-27) ?

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

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simplify-3sqrt(-27)

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

14 4^{- \frac{3}{2}}

\frac{3 π}{2} + \frac{5 π}{6}

(100 v^{\frac{2}{5}})^{\frac{3}{2}}

\frac{4 x}{( 3 x ^{3} ) ^{3}}

\frac{65}{121}