Final answer:
The value of the expression square root of 2 plus square root of 1/2 is simplified as (2√2 + 1)/2.
Step-by-step explanation:
To determine the value of the expression square root of 2 plus square root of 1/2, we first need to understand how to work with square roots and fractions. The square root of 2 is already in its simplest form, which is approximately 1.4142.
However, the square root of 1/2 needs simplification. Since the square root of 1/2 is the same as the square root of 1 divided by the square root of 2, we can simplify it to 1/√2. To add these two together, we can rationalize the denominator of the second term by multiplying both the numerator and denominator by √2, which gives us √2 + 1/√2 * √2/√2 = √2 + √2/2. This simplifies to (2√2 + 1)/2. Thus, the value of the original expression is (2√2 + 1)/2.