Approximate the square root of a non-perfect decimal: What is a good decimal approximation for √0.9?

Introduction / Context:
Some square roots are irrational and must be approximated. √0.9 is slightly less than 1, and a reasonable decimal approximation is required among the choices provided.

Given Data / Assumptions:

• We compare the options to the true value of √0.9.
• 0.9 is near 1; the root should be near 1 but smaller.

Concept / Approach:
Use the idea that √(1 − ε) ≈ 1 − ε/2 for small ε. Here ε = 0.1, giving an estimate near 0.95. We then choose the closest option.

Step-by-Step Solution:

Verification / Alternative check:
Square 0.94: 0.8836 (a bit low). Square 0.95: 0.9025 (a bit high). The true value is between; 0.94 is the nearest available option.

Why Other Options Are Wrong:

• 0.3, 0.03, 0.33 are far too small.
• 0.9 is the radicand, not its square root.

Common Pitfalls:
Guessing 0.9 or 1; remember square roots compress values between 0 and 1 upward but remain below 1.

Final Answer:
0.94