Find an approximate value of the square root of 5 to the nearest tenth.

Answer

To find an approximate value of the square root of 5 to the nearest tenth, we first determine which two whole numbers it lies between. Since 2 squared is 4 and 3 squared is 9, the square root of 5 lies between 2 and 3. Next, we test decimals between 2 and 3 to find which two tenths the square root of 5 lies between. We square each tenth: 2.1 squared = 4.41, 2.2 squared = 4.84, and 2.3 squared = 5.29. Since 4.84 is less than 5 and 5.29 is greater than 5, the square root of 5 lies between 2.2 and 2.3. To round to the nearest tenth, we look at the midpoint, which is 2.25. Since 2.25 squared is 5.0625, and 5 is less than 5.0625, the value of the square root of 5 is less than 2.25. Therefore, rounded to the nearest tenth, the approximate value is 2.2.