The value of $\sqrt{2}$ upto three places of decimal is

Concept & Fact The square roots of small non-perfect square integers are irrational numbers. Their approximate decimal values up to three decimal places are standard mathematical constants that must be memorized for competitive exams. Step-by-Step Solution * The question directly asks for the factual decimal value of $\sqrt{2}$. * While you can calculate it using the long division method for square roots, competitive exams require rote memorization of this specific value. * The exact value is an infinite, non-repeating decimal: $1.41421356...$ * Rounding or truncating this to three decimal places yields $1.414$. * Comparing this to the given options, $1.414$ matches option (d). Exam Strategy & Shortcut There is no calculation shortcut; the strategy is purely memorization. You must commit the following core values to memory to save time in geometry and mensuration problems: $\sqrt{2} \approx 1.414$ $\sqrt{3} \approx 1.732$ $\sqrt{5} \approx 2.236$ Common Pitfall Students who haven't memorized the value might attempt to estimate it by squaring the options (e.g., $1.41^2$). While $1.4 \times 1.4 = 1.96$, attempting to manually multiply $1.412 \times 1.412$ under time pressure consumes valuable minutes and often leads to arithmetic mistakes. Final Answer Therefore, the correct answer is **1.414**.