Find the value of square root of 30 to one decimal place without a calculutor

To find the square root of 30 to one decimal place without using a calculator, we can use estimation and approximation. First, let's find two perfect square numbers that are closest to but smaller and larger than 30. The perfect square numbers closest to 30 are 25 (5^2) and 36 (6^2). Since 30 is closer to 25 than 36, we can start with the approximation of the square root of 30 as being close to the square root of 25, which is 5. To refine this approximation and get a more accurate value, we can perform a simple calculation using the average of this approximation and the number we want to find the square root of. Average = (Approximation + (30 / Approximation)) / 2 Using our initial approximation of 5: Average = (5 + (30 / 5)) / 2 Average = (5 + 6) / 2 Average = 11 / 2 Average = 5.5 The average value of 5.5 is a refined approximation of the square root of 30. Therefore, the square root of 30, rounded to one decimal place, is approximately 5.5.