How to Rationalize the Denominator of 6 - 4√2 / 6 + 4 √2

To rationalize the denominator of a fraction means to eliminate any radical expressions (like square roots) from the denominator. This is typically done by multiplying both the numerator and the denominator of the fraction by a suitable factor. General Process Identify the radical in the denominator: Determine the radical expression that needs to be removed. Multiply by a conjugate (if needed): If the denominator is a binomial with a radical (e.g., √a + √b or √a - √b), multiply both the numerator and denominator by its conjugate. The conjugate of (√a + √b) is (√a - √b), and vice versa. Simplify: After multiplying, simplify the expression by performing the necessary operations (like squaring) and combining like terms. Example Let's say we have the fraction 1/√2. To rationalize the denominator: Identify the radical: The radical is √2. Multiply by a conjugate: Since the denominator is a monomial, we multiply both numerator and denominator by √2