Simplify \( \sqrt{(a+b)^{2}} \) \( a^{2}+b^{2} \) \( a b \) \( a+b \)

We are given four separate expressions to simplify. Here’s how to simplify each one: 1. √((a + b)²) The square root of a square is the absolute value. In general, for any real number x, √(x²) = |x|. Thus, √((a + b)²) = |a + b|. 2. a² + b² The sum a² + b² is already in its simplest form. (Note that unless additional conditions or factorizations involving complex numbers are considered, there is no simpler real form.) 3. ab The product ab is already as simple as it can be. 4. a + b The sum a + b is also already in simplest form. So the simplified forms are: • √((a + b)²) = |a + b| • a² + b² remains as a² + b² • ab remains as ab • a + b remains as a + b