Approximate square of a decimal: Compute (9.2)^2 to the nearest option.

Introduction / Context:Squaring a decimal near 10 can be done quickly by the identity (a − b)^2 = a^2 − 2ab + b^2 with a convenient anchor, such as a = 10 and b = 0.8 for 9.2. This keeps mental arithmetic manageable and accurate to within a small margin.

Given Data / Assumptions:

• We need (9.2)^2
• Compare to options to select the closest

Concept / Approach:Use 9.2 = 10 − 0.8. Then (10 − 0.8)^2 = 100 − 2*10*0.8 + 0.8^2 = 100 − 16 + 0.64 = 84.64. The nearest provided option is 90 (difference 5.36) versus 75 (difference 9.64).

Step-by-Step Solution:

Verification / Alternative check:Direct multiplication: 9.2 × 9.2 = 84.64 confirms the identity method. The options are coarse, so select the nearest.

Why Other Options Are Wrong:

• 75: too low by nearly 10.
• 110, 125: far above the true square.
• 85: closer than 75, but still farther than 90 from 84.64.

Common Pitfalls:Rounding 9.2 to 9 or 10 without compensating can overshoot. Using the binomial square keeps the approximation tight.

Final Answer:90