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
#1:
Instructions: simplify each.
$$a)\hspace{.2em}\sqrt{-50}$$
$$b)\hspace{.2em}\sqrt{-304}$$
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#2:
Instructions: simplify each.
$$a)\hspace{.2em}\sqrt{-5}\cdot \sqrt{-5}$$
$$b)\hspace{.2em}\sqrt{-2}\cdot \sqrt{-8}\cdot \sqrt{-6}$$
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#3:
Instructions: simplify each.
$$a)\hspace{.2em}\sqrt{-55}\cdot \sqrt{-11}$$
$$b)\hspace{.2em}\sqrt{-3}\cdot \sqrt{21}$$
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#4:
Instructions: simplify each.
$$a)\hspace{.2em}\sqrt{-20}\cdot \sqrt{-2}\cdot \sqrt{-5}$$
$$b)\hspace{.2em}\frac{3\sqrt{-50}}{\sqrt{-5}}$$
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#5:
Instructions: simplify each.
$$a)\hspace{.2em}\frac{-5\sqrt{-40}}{\sqrt{8}}$$
$$b)\hspace{.2em}\frac{-2\sqrt{-20}}{\sqrt{-10}}\cdot \sqrt{-15}$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}5i\sqrt{2}$$
$$b)\hspace{.2em}4i\sqrt{19}$$
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#2:
Solutions:
$$a)\hspace{.2em}{-}5$$
$$b)\hspace{.2em}{-}4i\sqrt{6}$$
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#3:
Solutions:
$$a)\hspace{.2em}{-}11\sqrt{5}$$
$$b)\hspace{.2em}3i\sqrt{7}$$
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#4:
Solutions:
$$a)\hspace{.2em}{-}10i\sqrt{2}$$
$$b)\hspace{.2em}3\sqrt{10}$$
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#5:
Solutions:
$$a)\hspace{.2em}{-}5i\sqrt{5}$$
$$b)\hspace{.2em}{-}2i\sqrt{30}$$
