Final answer:
To rationalize the fraction 1/√2, you multiply the numerator and denominator by √2. This eliminates the radical in the denominator, resulting in the rationalized form √2/2, which is option (a).
Step-by-step explanation:
To rationalize the denominator of the fraction 1/√2, we need to eliminate the radical (the square root) from the denominator. This is a common practice in mathematics to make the expression easier to work with.
We start by multiplying the numerator and the denominator by the radical present in the denominator; in this case, we multiply by √2. This is because multiplying a radical by itself gives us the number under the radical. So, √2 × √2 = 2.
Here's the step-by-step process:
- Multiply the numerator and denominator by √2.
- The fraction becomes (1 × √2) / (√2 × √2).
- Simplify the expression to get √2 / 2.
Therefore, the rationalized form of 1/√2 is √2/2, which corresponds to option (a).
This process of rationalizing the denominator makes it easier to add, subtract, multiply, and divide fractions that contain radicals. This is particularly helpful when dealing with geometry, algebra, and calculus problems.