Questions: Multiply. [ (sqrt-9)(sqrt-49) ] [ (sqrt-9)(sqrt-49)= ] (Simplify your answer.)

Transcript text: Multiply. \[ (\sqrt{-9})(\sqrt{-49}) \] \[ (\sqrt{-9})(\sqrt{-49})= \] $\square$ (Simplify your answer.)

Solution

Step 1: Recognize the multiplication of two complex numbers

Given two complex numbers in the form of $\sqrt{-a} \cdot \sqrt{-b}$, where $a$ and $b$ are non-negative real numbers.

Step 2: Convert to imaginary form using $\sqrt{-a} = i\sqrt{a}$ and $\sqrt{-b} = i\sqrt{b}$

This gives us $i\sqrt{a} \cdot i\sqrt{b}$.

Step 3: Multiply the expressions

Multiplying the expressions gives us $i^2\sqrt{ab}$.

Step 4: Simplify using $i^2 = -1$

This simplifies to $-\sqrt{ab}$.

The result of multiplying $\sqrt{-9}$ and $\sqrt{-49}$ is $-\sqrt{441}$ = -21.

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