Here are the essential concepts you must grasp in order to answer the question correctly.
Radicals
Radicals are expressions that involve roots, such as square roots, cube roots, etc. In this context, we are dealing with square roots, which are denoted by the radical symbol (√). Understanding how to simplify radicals is crucial, as it allows us to express them in their simplest form, making it easier to perform operations like addition and subtraction.
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Like Radicals
Like radicals are terms that have the same radicand (the number under the radical) and the same index. For example, √12 and √75 are not like radicals because their radicands differ. To add or subtract radicals, it is essential to simplify them to like radicals, which can then be combined by adding or subtracting their coefficients.
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Adding & Subtracting Like Radicals
Simplifying Radicals
Simplifying radicals involves breaking down the radicand into its prime factors and identifying perfect squares. For instance, √12 can be simplified to 2√3, as 12 = 4 × 3 and √4 = 2. This process is necessary to express radicals in their simplest form, allowing for easier addition or subtraction of terms.
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Adding & Subtracting Unlike Radicals by Simplifying