What is the BEST approximation of square root of 11 to the nearest tenth?

Answer

To find the best approximation of the square root of 11 to the nearest tenth, we first look for the two perfect squares that 11 falls between. The perfect square less than 11 is 9 (3 squared) and the perfect square greater than 11 is 16 (4 squared). Therefore, the square root of 11 must be between 3 and 4. We can test decimals between 3 and 4 to find a closer approximation: 3.3 squared = 10.89 and 3.4 squared = 11.56. Since 10.89 is closer to 11 than 11.56 is (11 minus 10.89 = 0.11, while 11.56 minus 11 = 0.56), the value is approximately 3.3.