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Radical expressions and absolute value

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Keep in mind that if an entire equation is under a radical sign, such as 4 + 9, we first add the two terms together, and then place the result under the radical sign. Therefore, we would write 13 under a radical sign. On the other hand, if we have an equation, and each term is under a distinct equals sign, such as 4 + 4, with each 4 under a distinct radical sign, we find the square root of each term individually before we add them together. Therefore, our answer would be 4 because the square root of 4 is 2. We turn each 4 into a 2 and then add the two 2s together in order to get our 4.

Absolute value is also very important to keep in mind when dealing with radical expressions. It is only sometimes correct to say that the square root of a term squared equals the base. In other words, it is only sometimes correct to say that the square root of x^2 = 2. Sometimes it is not correct. Therefore, we would do better to say that the square root of x^2 = |x|. This is because the square root of (-4)^2, for example, is not -2. It is 2.

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