sqrt8

sqrt(8) denotes the principal square root of 8, the nonnegative real number whose square equals 8. In simplest radical form, sqrt(8) can be simplified by factoring the radicand: 8 = 4 × 2, so sqrt(8) = sqrt(4) × sqrt(2) = 2√2.

As a decimal, sqrt(8) is approximately 2.8284271247461903, and is often rounded to 2.828. The value is irrational, since √2 is irrational and multiplying by a nonzero rational number preserves irrationality.

Geometrically, sqrt(8) is the length of the diagonal of a square with side length 2, and it also equals the magnitude of the vector (2, 2). In algebraic contexts, expressing sqrt(8) as 2√2 can simplify calculations and help combine like terms or rationalize denominators.

The concept sits among radical simplification and irrational numbers. A general rule relevant here is that sqrt(ab) = sqrt(a) sqrt(b) for nonnegative a and b, which explains why 8 can be written as 4×2 and pulled apart as 2√2. See also √2 and Pythagoras’ theorem for related geometric interpretations.