Multiple choice

Find the approximate value of the equations: (50.01^2 + 19.999^2 + \text{?} = 50.998^2)

  1. $-489$
  2. $-299$
  3. $-363$
  4. $-456$
  5. $-350$
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B Correct answer
Explanation

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.

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