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  • The Largest Integer for which n^200<5^300 is
Multiple choice general knowledge math & puzzles

The Largest Integer for which n^200<5^300 is

  1. 8

  2. 9

  3. 10

  4. 11

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

n^200 < 5^300. Taking the 200th root of both sides: n < 5^(300/200) = 5^(3/2) = √125 ≈ 11.18. Since n must be an integer, the largest value is n = 11. Verification: 11^200 = (11^2)^100 = 121^100, while 5^300 = (5^3)^100 = 125^100. Since 121 < 125, 11^200 < 5^300 holds true.

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