What is $\sqrt{14}$? Round your answer to the nearest hundredth (two decimal places).
Answer (1)
Calculate the square root of 14: 14 ≈ 3.741657 .
Round the result to the nearest hundredth: 3.741657 ≈ 3.74 .
The square root of 14 rounded to the nearest hundredth is 3.74 .
Explanation
Understanding the Problem We are asked to find the square root of 14 and round the result to the nearest hundredth (two decimal places). The square root of a number x is a value that, when multiplied by itself, equals x . In this case, we need to find a number y such that y 2 = 14 and then round y to the nearest hundredth.
Calculating the Square Root First, we calculate the square root of 14. The result of this operation is approximately 3.7416573867739413.
Rounding to Nearest Hundredth Next, we round the result to the nearest hundredth (two decimal places). Looking at the third decimal place, which is 1, we know that we should round down. Therefore, 3.7416573867739413 rounded to the nearest hundredth is 3.74.
Final Answer Therefore, 14 rounded to the nearest hundredth is 3.74.
Examples
Square roots are used in many real-world applications, such as calculating the distance between two points in a coordinate plane or determining the length of the side of a square given its area. For example, if you have a square garden with an area of 14 square meters, you can use the square root of 14 to find the length of each side, which would be approximately 3.74 meters. This concept is also fundamental in physics, engineering, and computer graphics.
