Question

In the following exercises, simplify. (a) $\sqrt[3]{27}$ (b) $\sqrt[4]{16}$ (c) $\sqrt[5]{243}$

   In the following exercises, simplify.
(a) $\sqrt[3]{27}$ (b) $\sqrt[4]{16}$ (c) $\sqrt[5]{243}$
Intermediate Algebra
Intermediate Algebra
Lynn Marecek 1st Edition
Chapter 8, Problem 12 ↓
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In the following exercises, simplify. (a) $\sqrt[3]{27}$ (b) $\sqrt[4]{16}$ (c) $\sqrt[5]{243}$
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Transcript

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00:01 Okay, we are asked here to simplify each of these expressions.
00:04 Now, how we read this here is what we call the cubed root of 27.
00:10 So the cubed root of 27 essentially means what number times itself three times, what number times itself three times will equal 27? well, we can kind of think about this in our head and take a few practice numbers.
00:27 We can start off small and say, well, does one times one? times 1 equal 27? definitely not.
00:35 What about 2 times 2 times 2? 2 times 2.
00:39 Does that equal 27? definitely not.
00:42 2 times 2 times 2 equals 8.
00:46 2 times 2 is 4, 4 times 2 is 8.
00:48 However, let's try 3 times 3 times 3.
00:52 Does that equal 27? or 3 times 3 is 9? 9 times 3 is 27.
00:58 So indeed, the cubed root of 27 is equal to 3 because 3 times 3 times 3 is 27.
01:13 Well, let's try the fourth root of 16, the fourth root, meaning what times what times what, what times what times what times what times what, four times equal 16.
01:29 Well, if you think about that, well, that would essentially be two times two times two, 2 times 2 is 4.
01:38 4 times 2 is 8...
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