Question

fill in each blank so that the resulting statement is true.
\\(\sqrt{-45} = \underline{\quad\quad} \sqrt{45} = \underline{\quad\quad} \sqrt{9 \cdot 5} = \underline{\quad\quad} \sqrt{5}\\)

fill in each answer box so that the resulting statement is true.
\\(\sqrt{-45} = \boxed{\quad} \sqrt{45} = \boxed{\quad} \sqrt{9 \cdot 5} = \boxed{\quad} \sqrt{5}\\)
(simplify your answer.)

Explanation:

Separate the negative sign

Using the Imaginary Numbers knowledge point

$$ \sqrt{-45} = i\sqrt{45} $$

Apply the product rule

Using the Product Rule for Radicals and Square Root Properties knowledge points

$$ i\sqrt{45} = i\sqrt{9 \cdot 5} = i\sqrt{9}\sqrt{5} = 3i\sqrt{5} $$

Answer:

Fill in each blank so that the resulting statement is true.
\(\sqrt{-45} =\) <blank>\(i\)</blank> \(\sqrt{45} =\) <blank>\(i\)</blank> \(\sqrt{9 \cdot 5} =\) <blank>\(3i\)</blank> \(\sqrt{5}\)