Q71. 39.98% of 249.99 + √196.04 = x² + 55.93

Question

Q71. 39.98% of 249.99 + √196.04 = x² + 55.93

1. A. 6
2. B. 9
3. C. 5
4. D. 8 (Correct answer)
5. E. 4

Correct Answer

Option D — 8

Detailed Solution & Explanation

The correct answer is 8.

Key Points

• Round each term and solve for x.
• 39.98% of 249.99 ≈ 40% of 250 = 100.
• √196.04 ≈ √196 = 14.
• So the left side ≈ 100 + 14 = 114, and the equation is 114 = x² + 55.93 ≈ x² + 56.
• Therefore x² ≈ 114 − 56 = 58, giving x ≈ √58 ≈ 7.6, which rounds to the nearest option 8.
• approximate the percentage and the square root first, isolate x², then take the square root.
• Knowing that √196 = 14 and that 58 lies between 7² = 49 and 8² = 64 (closer to 8) gives the answer quickly.

Exam Tip

• memorise perfect squares up to 20² so you can instantly bracket any square root between two integers.