Find each root. √12²

Verified step by step guidance

1. Recognize that the expression \( \sqrt{12^2} \) involves the square root of a squared number.
2. Recall the property that \( \sqrt{a^2} = |a| \), which means the square root of a square is the absolute value of the original number.
3. Apply this property to the expression: \( \sqrt{12^2} = |12| \).
4. Since 12 is positive, the absolute value \( |12| \) is simply 12.
5. Therefore, the root of the expression \( \sqrt{12^2} \) is 12.

Key Concepts

Order of Operations

The order of operations dictates the sequence in which mathematical operations should be performed to get the correct result. Typically, exponents are evaluated before roots or other operations. Understanding this helps in correctly simplifying expressions like √12².

Square and Square Root Relationship

Squaring a number means multiplying it by itself, while the square root is the inverse operation, finding a number that when squared gives the original value. Recognizing that √(a²) equals the absolute value of a is crucial for solving expressions involving squares and roots.

Simplifying Radicals

Simplifying radicals involves reducing the expression under the root to its simplest form or evaluating the root when possible. In this problem, understanding how to simplify √12² by applying the properties of exponents and roots is essential to find the correct root.