If $\sqrt{.00000676} = .0026$, the square root of $67,60,000$ is:

Concept & Logic The significant digits of a square root remain constant if the original number is multiplied by an even power of $10$. You can extract the integer square root and append the appropriate number of zeros. $$\sqrt{x \cdot 10^{2n}} = \sqrt{x} \cdot 10^n$$ Step-by-Step Solution * **Given:** $\sqrt{.00000676} = .0026$. By moving the decimal 8 places to the right (multiplying by $10^8$), we can deduce that the square root of the significant digits is $\sqrt{676} = 26$. * **Calculation:** We need to evaluate $\sqrt{6760000}$. * Break the number down into known perfect squares: $\sqrt{676 \times 10000}$. * Apply the square root separately to both parts: $\sqrt{676} \times \sqrt{10000}$. * Substitute the known values: $26 \times 100 = 2600$. Exam Strategy & Shortcut Count the trailing zeros. The number $6760000$ has $4$ trailing zeros. Its square root will have exactly half that number of trailing zeros, which is $2$. The significant integer part is $\sqrt{676} = 26$, so simply attach two zeros to get $2600$. Common Pitfall Overcomplicating the problem by trying to reverse-engineer the decimal shift from the given equation, rather than just extracting the core significant root ($\sqrt{676} = 26$) and solving the new number independently. Final Answer **Therefore, the correct answer is 2600.**