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In algebraic expressions, the term "double negative" refers to a situation where two negative signs are used in close succession. These often cancel each other out and effectively create a positive. For example, if you encounter something like

• \( -(-a) \) it simplifies to \( +a \).

Think of it as the rule for multiplying negative numbers: two negative numbers multiplied together form a positive. This is because mathematically, a negative sign indicates a reversal of the direction. Reversing twice returns to the original direction, hence positive.
In the original exercise, the expression \(16--\sqrt{5}---1\) simplifies as follows: -\(\sqrt{5}\) is negated twice, which gives \(+\sqrt{5}\), and similarly, -1 is negated thrice, which compensation results in added 1. Thus, the expression simplifies to \(16 + \sqrt{5} + 1\).

Understanding square root simplification is essential in performing various algebraic operations. A square root, represented by the radical symbol \(\sqrt{}\), is a value that, when multiplied by itself, gives the original number. For example:

• \( \sqrt{4} = 2 \) because \(2 \times 2 = 4\).
• \( \sqrt{9} = 3 \) since \(3 \times 3 = 9\).

Not all square roots are perfect squares, though. For example, \(\sqrt{5}\) cannot be simplified to a whole number. In algebra, when dealing with non-perfect square roots such as \(\sqrt{5}\), leave it as it is unless it is paired or simplified further mathematically. The main aim is to ensure the expression is in its simplest form. In the given exercise, the focus is on the structure, so \(\sqrt{5}\) remains unchanged beyond removing the double negative.

The concept of "addition of like terms" is integral in simplifying algebraic expressions. Like terms contain the same variable raised to the same power. When adding them, only the coefficients are added while the variable part remains unchanged.
In our exercise:

• The like terms are numbers without variables, which are 16 and 1.
• By adding these together, such as \(16 + 1 = 17\), you simplify the expression.

Therefore, the final simplified expression is \(17 + \sqrt{5}\). This indicates combining of constant numbers only. The variable term \(\sqrt{5}\) has no like terms to combine with, hence it remains part of the expression, yielding \(17 + \sqrt{5}\) as the final answer.