ShmoopTube

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Roots, a la Shmoop. In 1976, Alex Haley published a popular and

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award-winning novel about race, emancipation and basic human rights...

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Oh, so the book isn't what we're talking about right now?

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Sorry, our bad. There we go.

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Apparently, you're here to learn about an entirely different type of root.

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Let's look at an example. Here's the square root of 9.

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It's just the number 9 inside of a funny-looking symbol that resembles a checkmark.

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Here's what this symbol is asking: "What number, when multiplied by itself, equals 9?"

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Well, if you've ever drawn a Tic-Tac-Toe board, you should know that the answer is 3.

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A root is really just the opposite of an exponent... ... 3 squared equals 9, and the square root

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of 9 equals 3. Things get more complicated, however. Oh,

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goody. Not every root is a square root. You can also

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have a cubed root. Like this one: The 3 is telling you there is a number that

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will fit this formula: You can plug in "2" to make this equation

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complete, so we can say that 2 is the cube root of 8.

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You can do the same with higher roots as well, although you are now entering serious headache

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territory. If you don't feel like drawing the root symbol,

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roots can also be expressed as exponents. If something is raised to the power of one-half,

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it's the same as a square root. If it has an exponent of one-third, then we're

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dealing with a cube root. Be careful, though, when negative numbers

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enter the picture.

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Those guys can mess you up. For example, there can never be a square root

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of a negative, as multiplying any two numbers always gives you a positive result.

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You CAN, however, have a cube root of a negative number.

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We know there are a lot of rules to keep in mind... We hope this video wasn't too painful

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for you... ...At least not as painful as a root canal.

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Guess we'll stop drilling you...for now.

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