sqrtLg10100

sqrtLg10100 is a compact mathematical expression that combines the square root function, the base-10 logarithm, and the positive integer 10100. In many contexts, Lg denotes the base-10 logarithm (also written log10). The expression thus reads as the square root of the common logarithm of 10100, i.e., sqrt(log10(10100)).

Evaluating it directly: log10(10100) can be simplified since 10100 = 101 × 100. Therefore log10(10100) = log10(101) + log10(100) = log10(101) + 2. Since log10(101) ≈ 2.00432137378, we obtain log10(10100) ≈ 4.00432137378. Taking the square root yields sqrt(4.00432137378) ≈ 2.0010800507. In practice, this is often rounded to about 2.0011.

Domain and interpretation: The expression is defined for positive arguments inside the logarithm; here 10100 > 0, so the result is a real number. If the argument inside the logarithm were 0 or negative, the logarithm would be undefined in the real numbers, and the square root would be undefined without extending to complex numbers. Notationally, some texts use log or log10 instead of Lg, so explicit parentheses are helpful: sqrt(Lg(10100)) or sqrt(log10(10100)).

Related concepts include the common logarithm, the square root function, and notation conventions for base-10 logarithms. The term is largely a straightforward application of these standard functions.