Questions: Divide as indicated. (sqrt(-105))/(sqrt(7))

Solution Steps

To solve the given problem, we need to simplify the expression by dividing the square roots. We can use the property of square roots that states \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\). After simplifying the fraction inside the square root, we can determine if the result is a real or complex number.

We start by simplifying the fraction inside the square root: \[ \frac{\sqrt{-105}}{\sqrt{7}} = \sqrt{\frac{-105}{7}} \] Simplifying the fraction inside the square root: \[ \frac{-105}{7} = -15 \]

Next, we calculate the square root of \(-15\). Since \(-15\) is a negative number, its square root will be an imaginary number: \[ \sqrt{-15} = \sqrt{15} \cdot i \] Approximating \(\sqrt{15}\) to four significant digits: \[ \sqrt{15} \approx 3.873 \] Thus: \[ \sqrt{-15} \approx 3.873i \]

Final Answer