39.98% of 249.99 + √196.04 = x2 + 55.93

Concept

In an approximation (≈) problem, replace each messy number with the nearest convenient round value, simplify the arithmetic, then isolate the unknown. Here the equation a% of b + √c = x2 + d is solved for x by collecting the left side and subtracting d from it.

Application

1. Round each term: 39.98% ≈ 40%, 249.99 ≈ 250, √196.04 ≈ √196 = 14, and 55.93 ≈ 56.

2. Compute 40% of 250 = 0.40 × 250 = 100.

3. Add the square-root term: 100 + 14 = 114, so the left side ≈ 114.

4. Set up the equation: 114 = x2 + 56.

5. Isolate x2: x2 = 114 − 56 = 58.

6. Take the square root: x = √58 ≈ 7.62.

Cross-check

Among the offered whole numbers, 7.62 is nearest to 8 (it is only 0.38 away, versus 1.62 from 7). Verify by substituting back: 82 + 56 = 64 + 56 = 120, which is the closest match to the left side ≈ 114 among the choices. So x ≈ 8.