sqrt25012000

The term sqrt(25012000) denotes the principal square root of 25,012,000. It is the nonnegative real number whose square equals 25,012,000.

Exact form and simplification: The prime factorization of 25,012,000 is 2^5 · 5^3 · 13^2 · 37. This enables extracting square factors: sqrt(25,012,000) = sqrt(2^4 · 5^2 · 13^2 · (2·5·37)) = 260√370. Thus the simplest exact expression is 260 times the square root of 370.

Decimal approximation: Evaluating numerically gives sqrt(25,012,000) ≈ 5,001.1998548. To three decimal places this is 5,001.200. The value lies between 5,001^2 = 25,010,001 and 5,002^2 = 25,020,004, as expected.

Properties and context: Because 370 is not a perfect square, sqrt(25,012,000) is irrational. The result reflects a common pattern in radical simplification: large integers can be expressed in a reduced radical form by factoring out perfect squares. The radical form 260√370 is typically preferred in exact arithmetic, while the decimal form is used for approximate calculations.

Applications: Values like sqrt(25,012,000) arise in geometry, physics, and engineering when exact radical forms are needed, or when assessing magnitudes that involve large square roots.