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How to Find the Fourth Root of a Number

How to Find the Fourth Root of a Number
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  • 0:03 What Is a Root?
  • 1:01 Finding the Fourth Root
  • 2:20 Symbols
  • 2:50 Examples
  • 4:08 Lesson Summary
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Lesson Transcript
Instructor: Stephanie Matalone

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

In this lesson, we'll go over the basics of roots and exponents, specifically discussing how to find fourth roots and how that relates to exponents. We will go over some specific examples as well.

What Is a Root?

Your teacher asks you to find the fourth root of the number 256. Your response. . . 'What?!?! I don't even know what that means!' No problem, let's start from the beginning. What does it mean to find the root of a number? When you see the word 'root', you should think of finding the square root.

Let's say I need to find the square root of 64. I am simply finding what number can be multiplied by itself to equal 64.

Finding the square root of a number is the opposite of squaring a number. In essence, we are a number that, when squared, equals the given number. In this case, we want to know what can be squared to give 64. Squaring a number is the same as using the exponent of 2 or something to the second power. For the number 64, we know that 8 times 8 will equal 64. Therefore, 8 squared (written 82), or eight to the second power, mean the same thing and equal 64.

Finding the Fourth Root

So, how does this relate to finding the fourth root of 256? Well, it's the same concept but instead of finding out what number can multiply by itself twice to give 256, we want to find out what number can multiply by itself 4 times to give 256.

Finding the fourth root of a number is the opposite of multiplying a number by itself 4 times. In other words, it's the opposite of using an exponent of 4. Let's look at it mathematically.

x4 = 256

To find the fourth root of 256, we need to figure out what x is in this equation. What number can we raise to the power of 4 to equal 256? Let's think about it. . . If I plug in 2, I will get the following:

24 = 2 x 2 x 2 x 2 = 16

Thus, obviously 2 is not the fourth root of 256. Let's jump up to the number 4.

44 = 4 x 4 x 4 x 4 = 256

4 multiplied by itself 4 times give us the number we are looking for, 256! Thus, the fourth root of 256 is equal to 4! Woohoo!! We solved it.

Symbols

We discussed the idea behind finding the fourth root of a number, but in mathpo/, we often have nifty symbols that tell us what to do. Whenever you see a radical symbol in math, you know you are dealing with roots. Radical symbols look like check marks with a horizontal line attached. The small number above the check mark portion (if there is one), called the index, tells you what root to find. The big number under the radical symbol as called the radicand and tells you what to take the root of.

fourthroot

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