sqrtx1x22y1y22z1z22

sqrtx1x22y1y22z1z22 is not a standard mathematical symbol. It appears to be a concatenation of the word sqrt with several subscripted terms x1, x2, y1, y2, z1, z2, and may be intended to denote a square root of a product involving those variables. Because the notation is ambiguous without parentheses, it is common to consider two readings.

One reading is sqrt(x1 x2 y1 y2 z1 z2), the square root of the product of six terms. In this reading, the expression is real-valued if the product x1 x2 y1 y2 z1 z2 is nonnegative; otherwise it takes a complex value. The square root distributes over a product only under certain conditions when working in the real numbers.

A second reading is the product of three square roots: sqrt(x1 x2) sqrt(y1 y2) sqrt(z1 z2). This interpretation requires each pair's product to be nonnegative in the real domain if real-valued results are desired. In general, sqrt(a b) = sqrt(a) sqrt(b) is valid for nonnegative a and b in the real numbers; for arbitrary signs or complex numbers, branch choices matter and the equality may fail.

In either interpretation, explicit parentheses are advised to avoid ambiguity. For example, sqrt((x1 x2)(y1 y2)(z1 z2)) equals sqrt(x1 x2 y1 y2 z1 z2) when the product is nonnegative. If complex values are allowed, one must specify branches of the square root.

Typical contexts include algebraic manipulation, geometric interpretations of products of coordinates, or programming notation where clarity about grouping is essential.