What is the square root of 1746 to four decimal places?

What is the square root of 1746 to four decimal places?

• A. 41.3050
• B. 41.9000
• C. 42.0000
• D. 41.7852

Answer: (D)

Finding a square root to four decimals means narrowing down the value by checking nearby squares. Since 41^2 = 1681 and 42^2 = 1764, the root of 1746 lies between 41 and 42. Testing refinements shows 41.785^2 = 1745.986225, which is just under 1746, so a touch more is needed. Using 41.7852, the square is 1746.00293904, which is just over 1746. The true root sits very close to 41.78516, so when rounded to four decimal places it becomes 41.7852.

Finding a square root to four decimals means narrowing down the value by checking nearby squares. Since 41^2 = 1681 and 42^2 = 1764, the root of 1746 lies between 41 and 42. Testing refinements shows 41.785^2 = 1745.986225, which is just under 1746, so a touch more is needed. Using 41.7852, the square is 1746.00293904, which is just over 1746. The true root sits very close to 41.78516, so when rounded to four decimal places it becomes 41.7852.