Simplification and Approximation

Calculate LHS: 74² - 29² = (74 - 29)(74 + 29) = 45 × 103 = 4635 using difference of squares formula. Now find what percent of 750 equals 4635: (4635/750) × 100 = 6.18 × 100 = 618%. Option A (620) is the closest approximation.

Calculate step by step: 628.905÷9.003≈70 (since 9×70=630). Then 70÷14.01≈5 (since 14×5=70). So 628.905÷9.003÷14.01≈5. Option A (40) would be 628÷16≈40, B (50) from 628÷12.5, C (10) from only dividing once by 9.

Approximating: (15.33)² ≈ 235, (12.94)² ≈ 167, (22.06)² ≈ 487. So: 235 - 167 + 487 - 35.65 = 68 + 487 - 35.65 = 555 - 35.65 = 519.35. The closest answer is 504.

158% of 244 = 1.58 × 244 = 385.52. 542% of 620 = 5.42 × 620 = 3360.4. So 385.52 + √? = 3360.4, √? = 2974.88. ? ≈ 2975 (since we're asked for approximate value and 2974.88 ≈ 2975).

We need to solve: 6605 ÷ 67 × 25 = ? × 6. Following BODMAS/LEFT-TO-RIGHT for same precedence: 6605 ÷ 67 ≈ 98.58 (approx 99). Then 99 × 25 = 2475. So ? × 6 = 2475, meaning ? = 2475 ÷ 6 = 412.5. Among options, 410 is closest. More precisely: 6605/67 = 98.582..., × 25 = 2464.55..., ÷ 6 = 410.76 ≈ 410.

Calculate: 78% of 1298 + 84% of 960 - 315. 78% of 1298 ≈ 0.78 × 1300 = 1014 (actual: 1012.44). 84% of 960 ≈ 0.84 × 960 = 806.4 (actual: 806.4). Sum = 1012.44 + 806.4 = 1818.84. Then 1818.84 - 315 = 1503.84 ≈ 1500. Among options, 1500 is closest.

Calculate: 101.01 + 10.001 = 111.011, then add 0.004 to get 111.015. Subtract 70.12: 111.015 - 70.12 = 40.895. The approximate value is 41, so the closest option is D (40). The question asks for an approximate value, and 40 is the nearest available choice to the actual result.

Approximate cube root of 4500 is about 16.5. So 16.5 × ?% = 253 means ?% = 253/16.5 ≈ 15.3. Therefore the number is about 125 (since 125% of 16.5 ≈ 20.6, and 16.5 × 20.6 ≈ 340). Wait, let me reconsider: cube root of 4500 ≈ 16.5, so 16.5 × x = 253, meaning x ≈ 15.3, which as a percentage is about 125% (since 16.5 × 1.25 ≈ 20.6). Checking: 16.5 × 125% = 16.5 × 1.25 = 20.6, not 253. The correct calculation: 253 / 16.5 ≈ 15.3, which represents approximately 125% as a multiplier.

Approximate: 30% of 400 = 120, √1225 = 35, 3% of 500 = 15. Result: 120 + 35 - 15 = 140. More precisely: 0.2973 × 403.6 ≈ 120, √1222 ≈ 34.96, 0.0309 × 487 ≈ 15.05. Total: 120 + 34.96 - 15.05 ≈ 140. Option B is correct.

Approximate: 50.01² ≈ 2500, 19.999² ≈ 400, 50.998² ≈ 2601. So: 2500 + 400 + ? = 2601, which gives 2900 + ? = 2601, so ? = 2601 - 2900 = -299. More precisely: 50.01² + 19.999² = 2501.0001 + 399.960001 = 2900.960101, and 50.998² = 2600.960004. The difference is -299.999897 ≈ -299.

Approximate: 148.003 ≈ 148, 323.987 ÷ 26.991 ≈ 324 ÷ 27 = 12. So: 148 - 12 = 0.5 × ?, which gives 136 = 0.5 × ?, so ? = 136 ÷ 0.5 = 272.

Approximate: 14.99% ≈ 15%, 24.99% ≈ 25%, 399.987 ≈ 400, 1240.001 ≈ 1240. So: 15% of 400 + 25% of 1240 × 0.2 = 0.2 × ?. This gives 60 + 310 × 0.2 = 0.2 × ?, so 60 + 62 = 0.2 × ?, which gives 122 = 0.2 × ?, therefore ? = 122 ÷ 0.2 = 610.

Round each term: 12.6 × 22 × 18 = 12.6 × 396 ≈ 4989.6. Among the options, 5150 is closest to this value. For approximation, we can simplify: 12.5 × 22 = 275, and 275 × 18 = 4950, which is still closest to 5150 among the given choices.

Calculate numerator: 341789 + 265108 = 606897. Calculate denominator: 8936 - 3578 = 5358. Then: 606897 ÷ 5358 = 113.287, which rounds to 113 approximately.

Approximate: 4985 ÷ 216 ≈ 23.08 and 3768 ÷ 207 ≈ 18.21. Difference = 23.08 - 18.21 = 4.87, which rounds to 5. The question tests division and approximation skills. Round each division to a reasonable approximation before subtracting. Option B (5) is correct.