Find each square root. See Example 1. √100

Verified step by step guidance

1. Recognize that the problem asks for the square root of 100, which means finding a number that, when multiplied by itself, equals 100.
2. Recall the definition of the square root: if \(x^2 = a\), then \(x = \sqrt{a}\) or \(x = -\sqrt{a}\), where \(a\) is a non-negative number.
3. Identify perfect squares near 100 to help find the square root. Since \$10^2 = 100$, 10 is a candidate.
4. Write the square root expression as \(\sqrt{100} = 10\) or \(-10\), because both \$10^2\( and \)(-10)^2$ equal 100.
5. Conclude that the principal (non-negative) square root of 100 is 10, which is typically the value referred to by \(\sqrt{100}\).

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 because 10 × 10 = 100. It is denoted by the radical symbol (√).

Perfect Squares

Perfect squares are numbers that are squares of integers, such as 1, 4, 9, 16, and 100. Recognizing perfect squares helps quickly find their square roots without a calculator, as their roots are whole numbers.

Principal Square Root

The principal square root refers to the non-negative root of a number. Although both positive and negative values squared give the original number, the square root symbol (√) typically represents the positive root only.