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, to rationalize 30/√5, you would multiply by √5/√5.
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Rationalizing Denominators
Irrational Numbers
Irrational numbers are numbers that cannot be expressed as a simple fraction, meaning they cannot be written as the ratio of two integers. Common examples include square roots of non-perfect squares, such as √2 or √5. In the context of rationalizing denominators, the presence of an irrational number in the denominator is what necessitates the rationalization process.
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Multiplication of Fractions
Multiplication of fractions involves multiplying the numerators together and the denominators together. When rationalizing a denominator, this principle is applied to ensure that the fraction remains equivalent after multiplying by a form of one (like √5/√5). This step is crucial for maintaining the value of the original expression while transforming its form.
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