Find each square root. SeeExample 1.-√256

Verified step by step guidance

1. Identify the expression: You need to find the square root of 256, and then apply the negative sign.
2. Recall the definition of a square root: The square root of a number is a value that, when multiplied by itself, gives the original number.
3. Determine the positive square root of 256: Consider what number multiplied by itself equals 256.
4. Apply the negative sign: Once you have the positive square root, apply the negative sign to get the final result.
5. Verify your result: Ensure that when you square your final result, you get back to 256.

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 256 is 16, since 16 × 16 = 256. Square roots can be positive or negative, but the principal square root is typically the non-negative value.

Negative Square Roots

When dealing with negative square roots, it is important to recognize that the square root of a negative number is not a real number. Instead, it is expressed in terms of imaginary numbers. For instance, -√256 can be interpreted as -16, which is the negative of the principal square root of 256.

Radical Notation

Radical notation is a way to express roots using the radical symbol (√). The expression √x denotes the principal square root of x. In the context of the question, -√256 indicates taking the square root of 256 and then applying a negative sign to the result, emphasizing the importance of order in operations.