Approximation with square roots: The square root of 0.4 is approximately equal to which of the following?

Introduction / Context:
Estimating square roots quickly is a valuable skill. We compare √0.4 with familiar reference values to pick the closest option.

Given Data / Assumptions:
Compute √0.4 approximately.

Concept / Approach:
Since 0.36 = 0.6^2 and 0.49 = 0.7^2, √0.4 should lie between 0.6 and 0.7, closer to 0.6 because 0.4 is nearer to 0.36 than 0.49.

Step-by-Step Solution:
0.6^2 = 0.36, 0.7^2 = 0.49.0.4 is 0.04 above 0.36 but 0.09 below 0.49, so the root is nearer to 0.6.Thus √0.4 ≈ 0.632..., which rounds closer to 0.6.

Verification / Alternative check:
Using a calculator, √0.4 ≈ 0.63246, confirming the nearest choice is 0.6.

Why Other Options Are Wrong:
0.7, 0.8, 0.9, 0.5 are further from the true value than 0.6.

Common Pitfalls:
Confusing √0.4 with 0.4/2 = 0.2 or assuming linearity of the square function near zero.

Final Answer:
0.6