### About The Imaginary Unit i:

The imaginary unit i can be used to simplify the square root of a negative number. When trying to use the product rule for radicals with two negative numbers, we find that we must convert these using the imaginary unit i first. We can then use our product rule for radicals.

Test Objectives
• Demonstrate the ability to simplify the square root of a negative number
• Demonstrate the ability to find the product of square roots with negative numbers
The Imaginary Unit i Practice Test:

#1:

Instructions: simplify each.

$$a)\hspace{.2em}\sqrt{-50}$$

$$b)\hspace{.2em}\sqrt{-304}$$

#2:

Instructions: simplify each.

$$a)\hspace{.2em}\sqrt{-5}\cdot \sqrt{-5}$$

$$b)\hspace{.2em}\sqrt{-2}\cdot \sqrt{-8}\cdot \sqrt{-6}$$

#3:

Instructions: simplify each.

$$a)\hspace{.2em}\sqrt{-55}\cdot \sqrt{-11}$$

$$b)\hspace{.2em}\sqrt{-3}\cdot \sqrt{21}$$

#4:

Instructions: simplify each.

$$a)\hspace{.2em}\sqrt{-20}\cdot \sqrt{-2}\cdot \sqrt{-5}$$

$$b)\hspace{.2em}\frac{3\sqrt{-50}}{\sqrt{-5}}$$

#5:

Instructions: simplify each.

$$a)\hspace{.2em}\frac{-5\sqrt{-40}}{\sqrt{8}}$$

$$b)\hspace{.2em}\frac{-2\sqrt{-20}}{\sqrt{-10}}\cdot \sqrt{-15}$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}5i\sqrt{2}$$

$$b)\hspace{.2em}4i\sqrt{19}$$

#2:

Solutions:

$$a)\hspace{.2em}-5$$

$$b)\hspace{.2em}-4i\sqrt{6}$$

#3:

Solutions:

$$a)\hspace{.2em}-11\sqrt{5}$$

$$b)\hspace{.2em}3i\sqrt{7}$$

#4:

Solutions:

$$a)\hspace{.2em}-10i\sqrt{2}$$

$$b)\hspace{.2em}3\sqrt{10}$$

#5:

Solutions:

$$a)\hspace{.2em}-5i\sqrt{5}$$

$$b)\hspace{.2em}-2i\sqrt{30}$$