Simplify, correct to three significant figures, (27.63)$^2$ - (12.37)$^2$

Analyze the question: We need to compute 27.63² − 12.37² and round the result to 3 significant figures.

Concept: Use the difference of two squares: a² − b² = (a − b)(a + b)

Solution:

• a = 27.63, b = 12.37
• a − b = 27.63 − 12.37 = 15.26
• a + b = 27.63 + 12.37 = 40.00

So: 27.63² − 12.37² = 15.26 × 40 = 610.4

Check by direct calculation:

• 27.63² = 763.4169
• 12.37² = 153.0169
• Difference = 610.4

Round to 3 significant figures: 610.4 → 610

Tip: When you see two squared numbers being subtracted, think "difference of two squares" first. Here, the sum came out as exactly 40, which made the calculation much easier. Whenever the numbers add up to a round figure, this is usually the intended shortcut in WASSCE.