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 binomial involving a square root, you can multiply by the conjugate of that binomial.
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Conjugate of a Binomial
The conjugate of a binomial expression is formed by changing the sign between 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 eliminates the square root in the denominator, making it easier to simplify the expression.
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Simplifying Radicals
Simplifying radicals involves reducing a square root or other root to its simplest form. This can include factoring out perfect squares from under the radical sign or rewriting the expression in a way that makes it easier to work with. Understanding how to simplify radicals is essential for effectively rationalizing denominators and simplifying expressions in algebra.
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