If s represents the smaller number you can write an equation for s like this s^2 + (s+1)^2 = 61 2s^2 + 2s - 60 = 0 (subtract 61, collect terms) s^2 + s - 30 = 0 (divide by 2) (s-5)(s+6) = 0 (factor)

**The smaller number is 5**.__Check__5^2 + 6^2 = 25 + 36 = 61 Consider that the two numbers are almost equal. Thus, the value 61 is about double the square of one of those equal numbers. √(61/2) ≈ 5.5. Since we are looking for consecutive integers, this value between 5 and 6 suggests that the two integers involved are 5 and 6. A quick check (25+36=61) reveals 5 to be the correct choice for the smaller number.