Questions: Multiply. √(-5) · √(-14)

Solution Steps

To multiply the square roots of negative numbers, we can use the property of imaginary numbers. Specifically, \(\sqrt{-a} = i\sqrt{a}\), where \(i\) is the imaginary unit. We can then multiply the resulting imaginary numbers.

We start by calculating the square roots of the negative numbers: \[ \sqrt{-5} = i\sqrt{5} \quad \text{and} \quad \sqrt{-14} = i\sqrt{14} \]

Next, we multiply the two results: \[ \sqrt{-5} \cdot \sqrt{-14} = (i\sqrt{5}) \cdot (i\sqrt{14}) = i^2 \cdot \sqrt{5} \cdot \sqrt{14} \] Since \(i^2 = -1\), we have: \[ -i \cdot \sqrt{5 \cdot 14} = -i \cdot \sqrt{70} \]

The final result can be expressed as: \[ \sqrt{-5} \cdot \sqrt{-14} = -\sqrt{70} \]

Final Answer