Mia's statement likely pertains to how radicals (square roots, cube roots, etc.) can affect the simplification and evaluation of expressions, especially when combined with addition. Here are a few key points regarding radicals in addition expressions:
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Like Terms: Just like with regular numbers, you can only combine radicals in addition when they are like terms. For example, you can add \( \sqrt{2} + 3\sqrt{2} \) to get \( 4\sqrt{2} \), but \( \sqrt{2} + \sqrt{3} \) cannot be simplified further.
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Simplification: Before adding expressions that involve radicals, it's often helpful to simplify the radicals if possible. For example, \( \sqrt{8} \) can be simplified to \( 2\sqrt{2} \) before attempting to combine it with other terms.
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Rationalizing the Denominator: Sometimes, especially in more complex expressions, you might encounter a scenario where you need to rationalize a denominator that involves a radical prior to performing an addition. For example, turning \( \frac{1}{\sqrt{2}} \) into \( \frac{\sqrt{2}}{2} \).
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Distribution: If a radical is outside of parentheses, make sure to distribute it if necessary before combining with other terms.
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Evaluate: If evaluating a given expression numerically, you can compute the values of the radicals separately before performing the addition.
If there's a specific expression or example Mia is referring to, please share it, and I can provide more detailed guidance!
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