sqrt2194×107

The expression sqrt2194×107 can be ambiguous because it lacks parentheses. In mathematics, it may be read as either the square root of the product 2194 and 107, written as sqrt(2194×107), or as the product of 107 and the square root of 2194, written as 107√2194.

Interpretation A: sqrt(2194×107) equals sqrt(234,758). The prime factorization of 2194 is 2×1097 and 107 is prime, so the product has no square factors other than 1. The simplest radical form is √234758, and its decimal approximation is about 484.518.

Interpretation B: 107√2194 equals 107 times the square root of 2194, or 107√2194. Since 2194 = 2×1097, this cannot be simplified to a rational multiple of a smaller radical. The decimal value is approximately 5,011.90.

Notes and context: The two interpretations yield very different numerical values, highlighting why clear notation is important. If a single value is intended, parentheses or explicit formatting (for example, sqrt(2194×107) or 107√2194) remove ambiguity. In exact form, interpretation A is √234758, and interpretation B is 107√2194.