What is (-2sqrt(-100))(9sqrt(81)) ?

The solution to (-2sqrt(-100))(9sqrt(81)) is -1620i

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simplify (-2sqrt(-100))(9sqrt(81))

simplify

(- 2 - 100) (981)

- 1620 i

Solution steps

(- 2 - 100) (981)

Apply rule:

(- a) = - a

(- 2 - 100) = - 2 - 100

= - 2 - 100 \cdot 981

81 = 9

= - 2 - 100 \cdot 9 \cdot 9

Prime factorization of

100 : 2^{2} \cdot 5^{2}

= - 2 - 2^{2} \cdot 5^{2} \cdot 9 \cdot 9

Apply radical rule:

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

- 2^{2} \cdot 5^{2} = 2^{2} - 5^{2}

= - 2 2^{2} - 5^{2} \cdot 9 \cdot 9

Apply radical rule:

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

2^{2} = 2

= - 2 \cdot 2 - 5^{2} \cdot 9 \cdot 9

5^{2} = 25

= - 2 \cdot 2 - 25 \cdot 9 \cdot 9

Multiply the numbers:

- 2 \cdot 2 \cdot 9 \cdot 9 = - 324

= - 324 - 25

Apply radical rule:

- a = a - 1

- 25 = 25 - 1

= - 32425 - 1

Apply imaginary number rule:

- 1 = i

= - 32425 i

25 = 5

= - 324 \cdot 5 i

Multiply the numbers:

- 324 \cdot 5 = - 1620

= - 1620 i

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What is (-2sqrt(-100))(9sqrt(81)) ?
The solution to (-2sqrt(-100))(9sqrt(81)) is -1620i