What is the square root of 325 rounded to the nearest tenth?
The Correct Answer and Explanation is:
The square root of 325 is approximately 18.027. Rounded to the nearest tenth, this becomes 18.0.
Explanation:
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 325 is the number xxx such that x2=325x^2 = 325×2=325.
To calculate the square root of 325 without using a calculator, you can use estimation methods. Here’s a step-by-step breakdown:
- Find Perfect Squares Near 325:
- The square of 18 is 182=32418^2 = 324182=324.
- The square of 19 is 192=36119^2 = 361192=361.
- Estimate More Precisely:
The square root of 325 is slightly greater than 18 because 325 is just a bit more than 324 (which is 18218^2182). To refine the estimate, you can use the method of averaging or a calculator for more precision. - Use a Calculator:
A calculator or more advanced methods (like the Newton-Raphson method) can provide the exact value, which is approximately 18.027. - Rounding:
The decimal part of 18.027 is 0.027, which is less than 0.05, so when rounded to the nearest tenth, the square root becomes 18.0.
Thus, the square root of 325, rounded to the nearest tenth, is 18.0.
