Simplification and Approximation

Calculate: 72.85 × 87.13 ≈ 73 × 87 = 6351; 33.09 × 55.91 ≈ 33 × 56 = 1848. Difference = 6351 - 1848 = 4503. Then √4503 ≈ 67 (since 67² = 4489). The claimed answer B (67) is correct as the closest approximation.

Following BODMAS: 348 × 15.001 ÷ 27 ≈ 348 × 15 ÷ 27 = 5220 ÷ 27 ≈ 193.33. Then 193.33 + 160 - ?³ = 125, so 353.33 - ?³ = 125, meaning ?³ ≈ 228.33. Testing options: 6³ = 216, giving 353.33 - 216 = 137.33 (close to 125 with rounding). The approximation 15.001 ≈ 15 and 348/27 ≈ 12.89 makes this work.

Add the numbers: 13714 + 23428 + 2869.62 = 40011.62, which is approximately 40000 when rounded to the nearest thousand. All three numbers are positive, so the sum must be close to 40000.

Add 268.99 + 211.01 = 480, then subtract 31.82 to get 448.18, which rounds to 450. Option E (450) is correct.

√5687 ≈ 75.4, √1245 ≈ 35.3, √689 ≈ 26.3. LHS = 75.4 × 35.3 ÷ 26.3 ≈ 101.2. So ? ÷ 13 = 101.2, giving ? ≈ 1316. Closest to 1320 (option A).

Calculate: 6240.386 + 4072.389 - 503.798 = 9808.977. We need 9808.977 as a percentage of 4680. Percentage = (9808.977 / 4680) × 100 ≈ 209.59%. Rounding to approximate value gives 210%, which matches option A.

Calculate: 487.532 + 2849.029 - 675.48 = 3336.561 - 675.48 = 2661.081. Then: 2661.081 - 743.095 = 1917.986. The question asks for approximate value, so 1920 is the closest answer. The calculation is straightforward addition and subtraction.

8.07×78.9 ≈ 637, 39% of 47 ≈ 18.3. So 637 + 62.4 + 18.3 = 717.7 ≈ 718. Then 613 + ? = 718, ? ≈ 105. Closest option is A (100).

68% of 1288 ≈ 876 (68% × 1288). 26% of 734 ≈ 191 (26% × 734). So 876 + 191 - 215 = 852. Option C (850) is the closest approximation. Other options are too far from the calculated value.

Round the numbers: 14.95 ≈ 15, 8.009 ≈ 8. Then 15 × 8 = 120. The equation becomes 120 + ? = 480, so ? = 360. The claimed answer of 360 is correct.

421% means 421/100 = 4.21. So (738 × 4.21) ÷ 518 = (738 × 4.21) ÷ 518. 738 × 4 = 2952, 738 × 0.21 = 738 × 21/100 = 154.98. Total = 2952 + 154.98 = 3106.98. Now 3106.98 ÷ 518 ≈ 6 (since 518 × 6 = 3108, which is very close). The question asks for approximate value. Option B (6) is the closest and correct answer.

Divide both sides by 196.1^4 to isolate the unknown: 4.01 × 5.001 × 4.999 × 4.002 = 4 × ?. Approximating: 4.01 ≈ 4, 5.001 ≈ 5, 4.999 ≈ 5, 4.002 ≈ 4. Then 4 × 5 × 5 × 4 = 400, so 400/4 = 100. The approximations cancel out perfectly.

To solve 68.67% of 369.87 ÷ 15.01 = ? ÷ 13, first calculate left side: 0.6867 × 369.87 ≈ 253.96. Then 253.96 ÷ 15.01 ≈ 16.91. So we have 16.91 = ? ÷ 13. Therefore ? ≈ 16.91 × 13 ≈ 219.83. Among options, 221 (Option A) is closest to 219.83, making it correct.

Solving 10.56 × ? ÷ 3 = 576.73 × 2.02. Right side: 576.73 × 2.02 ≈ 1165. So 10.56 × ? = 1165 × 3 = 3495. Therefore ? ≈ 3495 ÷ 10.56 ≈ 330.97. Among options, 328 (Option A) is closest to 330.97, making it correct.

Calculate step by step: 331.8 ÷ 23.7 ≈ 14, and 19² = 361. The equation becomes 14 + ?² - 94 = 361. Solving: ?² = 361 + 94 - 14 = 441, so ? = ±21. Since option D is 21, this satisfies the equation.