sqrt252

The square root of 252, written as sqrt(252), is the positive real number that, when squared, equals 252. It is the principal square root used in standard mathematical notation.

252 factors as 2^2 · 3^2 · 7. Because the factors 2^2 and 3^2 are perfect squares, they can be extracted from under the radical: sqrt(252) = sqrt(2^2 · 3^2 · 7) = sqrt(2^2) · sqrt(3^2) · sqrt(7) = 2 · 3 · sqrt(7) = 6 sqrt(7).

Numerically, sqrt(252) is approximately 15.8745. The value is irrational, since sqrt(7) is irrational and the product of a nonzero rational and an irrational number is irrational.

Algebraically, sqrt(252) is a root of the polynomial x^2 − 252 = 0, and it represents the positive root. The radical form 6 sqrt(7) is the standard simplified expression for this square root.

In context, sqrt(252) can arise in problems involving areas, diagonals, or lengths where the number 7 appears as a factor, and simplifying radical expressions often converts sqrt(252) to the form 6 sqrt(7).