Find each square root. See Example 1. √100

Verified step by step guidance

1. Identify the problem: We need to find the square root of 100.
2. Recall the definition of a square root: The square root of a number \( x \) is a number \( y \) such that \( y^2 = x \).
3. Consider perfect squares: 100 is a perfect square because it can be expressed as \( 10^2 \).
4. Determine the square root: Since \( 10^2 = 100 \), the square root of 100 is 10.
5. Verify the result: Check that \( 10 \times 10 = 100 \) to confirm that 10 is indeed the square root of 100.

Key Concepts

Square Root Definition

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 100 is 10, since 10 × 10 = 100. Square roots can be positive or negative, but by convention, the principal square root is the non-negative value.

Perfect Squares

A perfect square is an integer that is the square of another integer. For instance, 1, 4, 9, 16, and 25 are perfect squares because they can be expressed as 1², 2², 3², 4², and 5², respectively. Recognizing perfect squares helps in quickly identifying their square roots.

Radical Notation

Radical notation is a mathematical symbol used to denote the square root and other roots. The symbol '√' represents the square root, while '√x' indicates the square root of x. Understanding this notation is essential for solving problems involving roots and simplifying expressions.