Find each square root. See Example 1. -√256

Verified step by step guidance

1. Recognize that the expression -\(\sqrt{256}\) means the negative of the square root of 256.
2. Recall that the square root of a number x, written as \(\sqrt{x}\), is a value that when multiplied by itself gives x.
3. Calculate \(\sqrt{256}\) by finding the number which, when squared, equals 256.
4. Since 16 \(\times\) 16 = 256, we have \(\sqrt{256}\) = 16.
5. Apply the negative sign in front of the square root to get the final expression: -\(\sqrt{256}\) = -16.

Key Concepts

Square Roots

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 because 16 × 16 = 256. Square roots can be positive or negative, but the principal square root is usually taken as the positive value.

Negative Square Roots

When a negative sign precedes a square root, such as -√256, it means the negative of the principal square root. This is different from the square root of a negative number, which involves imaginary numbers. Here, -√256 equals -16, the negative of the positive root.

Simplifying Square Roots

Simplifying square roots involves finding the exact value or expressing the root in simplest radical form. For perfect squares like 256, the square root is an integer. Recognizing perfect squares helps quickly simplify roots without a calculator.