Chapter 8, Problem 1RE

Write each number as the product of a real number and i.

$\sqrt{-9}$

To determine

To calculate: The given number as the product of a real number and $i$.

Answer to Problem 1RE

Solution: $3i$

Explanation of Solution

Given: The provided number is $\sqrt{-9}$.

Calculation: Now, write the number as shown below:

$\sqrt{-9}=\sqrt{-1\cdot 9}$

As it is known that $\sqrt[k]{x\cdot y}=\sqrt[k]{x}\cdot \sqrt[k]{y},$

Therefore,

$\sqrt{-1\cdot 9}=\sqrt{-1}\cdot \sqrt{9}$

As it is also known that $\sqrt{-1}=i,$

$\begin{array}{c}\sqrt{-1}\cdot \sqrt{9}=i\cdot 3\\ =3i\end{array}$

Hence, the number $\sqrt{-9}$ is the product of a real number $i$ and $3i$.