Questions: Write the expression in terms of i and simplify. sqrt(-2) sqrt(-14)=

Transcript text: Write the expression in terms of $i$ and simplify. \[ \sqrt{-2} \sqrt{-14}= \]

Solution

Step 1: Recognize the use of the imaginary unit $i$

Given the expression $\sqrt{{-a}} \cdot \sqrt{{-b}}$, we can rewrite it using $i$ as follows:

Step 2: Rewrite the expression as $\sqrt{a \cdot b} \cdot i$

Substitute $a = 2$ and $b = 14$ into the expression to get $\sqrt{2 \cdot 14} \cdot i$.

Step 3: Simplify the expression under the square root if possible

Since $a \cdot b = 28$, we simplify the square root to get $\sqrt{28} \cdot i = 5.29i$.

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