Rationalizing the numerator refers to the process of rewriting a fraction so that the numerator (the top number) does not contain any radicals or irrational numbers. This is typically done in order to simplify the expression or make it easier to work with.
Rationalizing the numerator is necessary when working with certain types of equations or expressions, such as when solving quadratic equations or simplifying radical expressions. It allows for easier manipulation and computation.
The most common method for rationalizing the numerator is to multiply both the numerator and denominator of the fraction by the conjugate of the denominator. This eliminates the radical in the numerator and results in a simplified expression.
The conjugate of a denominator is the same expression with the opposite sign between the terms. For example, the conjugate of √a + b would be √a - b. When multiplying a fraction by its conjugate, the terms in the denominator will cancel out, leaving a rationalized numerator.
Yes, for a fraction such as 1/√2, the conjugate of the denominator √2 is √2. Multiplying both the numerator and denominator by √2 gives us (1√2)/(√2√2) which simplifies to √2/2, resulting in a rationalized numerator.