Provide an appropriate response.
-If $a0$ and $b0$, then $\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}$.

Name: Provide an appropriate response. -If $a>0$ and $b>0$, then $\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}$.
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Question

Provide an appropriate response.
-If $a>0$ and $b>0$, then $\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}$.

Quizplus · Accepted Answer

The square root of a negative number can be expressed as the product of $i$ (the imaginary unit) and the square root of the positive counterpart of that number. Therefore, $\sqrt{-a} = i\sqrt{a}$, and multiplying it by $\sqrt{b}$ gives $i\sqrt{ab}$.

Provide an Appropriate Response a>0a>0a>0 And b>0b>0b>0 , Then −a⋅b=iab\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}−a​⋅b​=iab​

Provide an Appropriate Response $a>0$ And $b>0$ , Then $\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}$