Rationalise
i.) $\frac{8}{3 \sqrt{2}}$
Answer (1)
Multiply the numerator and denominator by 2 .
Simplify the expression: 6 8 2 .
Reduce the fraction to its simplest form.
The rationalized expression is 3 4 2 .
Explanation
Understanding the Problem We are asked to rationalize the expression 3 2 8 . This means we want to eliminate the square root from the denominator.
Rationalizing the Denominator To rationalize the denominator, we multiply both the numerator and the denominator by 2 : 3 2 8 × 2 2 = 3 × 2 8 2 = 6 8 2 .
Simplifying the Expression Now we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 6 8 2 = 3 4 2 .
Final Answer Therefore, the rationalized form of the given expression is 3 4 2 .
Examples
Rationalizing the denominator is a technique used in various fields, such as physics and engineering, to simplify calculations and make expressions easier to work with. For example, when calculating impedance in electrical circuits or dealing with wave functions in quantum mechanics, rationalizing denominators can help in obtaining more manageable and interpretable results. This skill is also useful in simplifying complex numbers and algebraic expressions in higher mathematics.
