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Chapter 8: Problem 100

Explain how to add like radicals. Give an example with your explanation.

Short Answer

Expert verified
Like radicals are radicals that share the same radicand and index. They can be added by adding their coefficients in a way similar to the addition of like terms in algebra. An example of this would be that \(\sqrt{5}\) and \(2\sqrt{5}\) are like radicals, and they add up to \(3\sqrt{5}\)

Step by step solution

01

Understanding Like Radicals

Like radicals are radical expressions with the same radicand and same index. For instance, \(\sqrt{3}\) and \(2\sqrt{3}\) are like radicals, while \(\sqrt{3}\) and \(\sqrt{2}\) are not. This is because the former pair have the same radicand (3 in this case) and the same index (which is 2 (the default) for square roots).
02

Addition of Like Radicals

When adding like radicals, only the coefficients (the numbers in front of the radical sign) are added or subtracted and the result is then coupled with the original radical. It's like adding algebraic like terms. Therefore, if you have \(7\sqrt{3}\) and \(3\sqrt{3}\), they can be added because they are like radicals. Their coefficients (7 and 3) would be added to give 10, and then this is combined with the original radical, yielding \(10\sqrt{3}\).
03

Example of Adding Like Radicals

Let's consider an example of like radicals: \(\sqrt{5}\) and \(2\sqrt{5}\). Here, we can see that the radicand for both terms is 5, which makes them like radicals. So to add them, we add just the coefficients: 1 (the coefficient of \(\sqrt{5}\) is 1, as there's no number in front of it) and 2 (the coefficient of \(2\sqrt{5}\)) to get 3. The result is put together with the original radical to provide the answer: \(3\sqrt{5}\).

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