Square root of a small decimal: Compute √0.00059049 and select the exact decimal value.

Introduction / Context:
Recognizing digit patterns helps here: 59049 is a familiar square (243^2). We only need to account for decimal places correctly when taking the square root.

Given Data / Assumptions:

• Number: 0.00059049.
• We know 243^2 = 59049.

Concept / Approach:
If a^2 = 59049, then (a/10^k)^2 = 0.00059049 for the appropriate k. Count decimal places to determine the square-root shift.

Step-by-Step Solution:

Verification / Alternative check:
(0.0243)^2 = 0.00059049 (since 243^2 = 59049 and (10^4)^2 = 10^8).

Why Other Options Are Wrong:

• .243 squares to 0.059049 (ten times too large).
• .00243 squares to 0.0000059049 (ten times too small).
• .000243 is off by two decimal places for the square root.

Common Pitfalls:
Miscalculating decimal-place shifts when taking square roots. Count digits carefully.

Final Answer:
.0243