Which of these fractions is the closest approximation to √2?

Rather than chasing decimals, compare each SQUARE against 2: $(99/70{)}^2=9801/4900$ ≈ 2.000204, $(7/5{)}^2=1.96,(17/12{)}^2=289/144$ ≈ 2.006944 and $(41/29{)}^2=1681/841$ ≈ 1.998811. The square nearest to 2 is 9801/4900, so 99/70 ≈ 1.414286 is the best fit — it matches √2 = 1.414214 to four decimal places, while the runner-up 41/29 ≈ 1.413793 already differs in the fourth. Choosing the simplest-looking fraction, 7/5, is the trap; simplicity and accuracy are not the same thing.