Question

Rationalize the denominator 1/√2

Answer 1

To rationalize the denominator of 1/√2, multiply both the numerator and denominator by √2 to obtain √2/2. This process ensures the denominator is rationalized without changing the value of the fraction.

Step-by-step explanation:

To rationalize the denominator of the fraction 1/√2, we multiply the numerator and the denominator by √2. This process utilizes the property that a number multiplied by itself is a square, hence √2 × √2 equals 2.

Here's the step-by-step process:

1. Multiply the numerator and the denominator by √2: (1 × √2) / (√2 × √2)
2. Simplify the expression: √2 / 2
3. The fraction now has a rational denominator and is properly rationalized.

By rationalizing the denominator, we have not changed the value of the fraction but have represented it in a more standard form that is easier to work with, especially when performing additional arithmetic operations.