91Ó°ÊÓ

When working with radical expressions, one important element to understand is the radicand. The radicand is the number or expression located inside the radical symbol (√). It’s the value from which we want to extract the root.

In the exercise, the expression is \(-7 \sqrt{y^{2}-8}\). Here, the portion enclosed by the square root symbol, \(y^{2}-8\), is the radicand.

Radicands can be:

• Numbers, like √9 where 9 is the radicand.
• Variables, like √x where x is the radicand.
• More complex expressions, like our example where \(y^{2}-8\) is the radicand.
  

Recognizing the radicand is crucial as it determines what you are working with under the radical.

The index in a radical expression indicates the degree of the root you are taking. If no number is written, it’s understood to be a square root with an index of 2. The index is denoted as a small number in the upper left of the radical symbol.

For example, \( \sqrt[3]{x} \) is a cube root with an index of 3, whereas \( \sqrt{x} \) has an implicit index of 2.

In the given expression, \(-7 \sqrt{y^{2}-8}\), the index is 2 because it’s a square root, even though the 2 isn’t explicitly written. Hence, when you see such radicals without an index mentioned, you can safely assume the index is 2. Remember, the index determines the 'degree' of the root you are taking from the radicand.

A square root is a special type of root indicated by the radical symbol with an implicit index of 2. It represents a value that, when multiplied by itself, gives the original radicand.

For example:

• √9 = 3 because 3 × 3 = 9.
• √25 = 5 because 5 × 5 = 25.

In the expression \(-7 \sqrt{y^{2}-8}\), the square root operation involves finding a number which, when squared, equals the radicand \(y^{2}-8\).

Key points about square roots:

• The symbol √ indicates a square root.
• The index is commonly 2, even if not shown.
• The radicand is the value inside the √.
  

Understanding square roots is fundamental as they are among the most frequent radical expressions encountered in mathematics.