What is (-3sqrt(27))(sqrt(-81)) ?

The solution to (-3sqrt(27))(sqrt(-81)) is -81sqrt(3)i

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simplify (-3sqrt(27))(sqrt(-81))

simplify

(- 327) (- 81)

- 813 i

Solution steps

(- 327) (- 81)

(- 327) (- 81) = - (327) - 81

= - 327 - 81

27 = 33

= - 3 \cdot 33 - 81

- 81 = 3 - 27

= - 3 \cdot 333 - 27

Apply radical rule:

a a = a, a \geq 0

33 = 3

= - 3 \cdot 3 \cdot 3 - 27

Prime factorization of

27 : 3^{3}

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

Apply exponent rule:

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

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

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

Apply radical rule:

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

3^{2} = 3

= - 3 \cdot 3 \cdot 3 \cdot 3 - 3

Multiply the numbers:

- 3 \cdot 3 \cdot 3 \cdot 3 = - 81

= - 81 - 3

Apply radical rule:

- a = a - 1

- 3 = 3 - 1

= - 813 - 1

Apply imaginary number rule:

- 1 = i

= - 813 i

(3 - 2) (3 + 2)

(3 + i) (5 - i)

\frac{729}{81}

\frac{6}{\frac{2}{3}}

x^{3} - 15 - 5 x + 3 x^{2}

What is (-3sqrt(27))(sqrt(-81)) ?
The solution to (-3sqrt(27))(sqrt(-81)) is -81sqrt(3)i