3\4+radical2
To evaluate the expression 3/4 + √2, you'll need to perform the addition operation between the rational number 3/4 and the irrational number √2. Let's break it down step by step:
Step 1: Rationalize the denominator of the radical (√2)
The denominator of √2 is 1 since the square root of 2 can be written as √2/1.
To rationalize the denominator, multiply both the numerator and denominator of √2 by (√2/√2) (which is equal to 1) to eliminate the square root in the denominator.
This gives us (√2 * √2) / (√2 * 1), which simplifies to (2/1) or just 2.
Step 2: Add the rational number 3/4 and the rationalized radical number 2.
Now, we can add the rational number 3/4 and the rationalized radical number 2.
To add fractions, we need a common denominator. In this case, the common denominator is 4.
Therefore, we need to adjust the numerator and denominator of 2 to have a denominator of 4. Multiply both the numerator and denominator of 2 by 2 to get 4/2.
Now, we can add the fractions: 3/4 + 4/4 = 7/4.
Step 3: Simplify the resulting fraction, if necessary.
The fraction 7/4 cannot be simplified any further because 7 is a prime number, and 4 is already in its simplest form.
So, the final answer to 3/4 + √2 is 7/4.