Short Answer 
The expression ‚Äöaoa + ‚Äöaob = ‚Äöao(a + b) holds true in specific cases, particularly when either a or b equals zero. However, for positive values of a and b, the equality does not generally apply, suggesting the need for caution in assuming it holds universally.
Step 1: Understand the Expression
The expression you’re dealing with is ‚Äöaoa + ‚Äöaob = ‚Äöao(a + b). This means you need to analyze when the sum of the square roots of two numbers (a and b) is equal to the square root of the sum of those same numbers. Begin by establishing the values of a and b that you want to evaluate.
Step 2: Investigate the Case of Zero Values
Consider scenarios where either a or b equals zero. In these cases, the expression becomes simpler. For example:
- If a = 0 and b = 0, then ‚Äöao0 + ‚Äöao0 = ‚Äöao0, confirming the equality.
- If a = 0 and b > 0, then ‚Äöao0 + ‚Äöaob = ‚Äöaob, which also holds true.
- If a > 0 and b = 0, the result is similar: ‚Äöaoa + ‚Äöao0 = ‚Äöaoa.
Step 3: Confirm the General Case
In situations where both a and b are greater than zero, the equation may not hold true in general. Therefore, it’s essential to conclude that while individual cases of zero work, the assumption doesn’t apply universally. Consider checking specific examples or conditions where the expression might yield valid results.