Here are the essential concepts you must grasp in order to answer the question correctly.
Rationalizing the Denominator
Rationalizing the denominator involves eliminating any irrational numbers from the denominator of a fraction. This is typically achieved by multiplying both the numerator and the denominator by a suitable expression that will result in a rational number in the denominator. For example, if the denominator is a sum of square roots, you can multiply by the conjugate of that expression.
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Rationalizing Denominators
Conjugates
The conjugate of a binomial expression is formed by changing the sign between the two terms. For instance, the conjugate of (a + b) is (a - b). When multiplying a binomial by its conjugate, the result is a difference of squares, which simplifies the expression and is particularly useful in rationalizing denominators that contain square roots.
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Simplifying Radicals
Simplifying radicals involves reducing a square root expression to its simplest form. This includes factoring out perfect squares from under the radical sign and rewriting the expression. For example, √12 can be simplified to 2√3, making calculations easier and clearer when working with expressions that include square roots.
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