What is the square root of 325 rounded to two decimal places?
The Correct Answer and Explanation is:
The square root of 325 rounded to two decimal places is 18.03.
Explanation
The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we are finding the square root of 325. Using a calculator or long division method, the exact value of √325 is approximately 18.027756…. When this is rounded to two decimal places, the result is 18.03.
To understand this better, let’s place it in the context of nearby perfect squares:
- √324 = 18 (since 18 × 18 = 324)
- √325 is slightly more than 18.
- √326 would be slightly more than √325.
This tells us that √325 falls between √324 and √326. Since √324 = 18 and √325 is just one more than 324, it makes sense that √325 is just a little more than 18. Specifically, it’s about 18.0277, which rounds up to 18.03.
Now let’s consider how we get to that value:
If you use a calculator:
- Inputting √325 gives you approximately 18.027756.
If you use estimation:
- Try squaring numbers close to 18. For example:
- 18 × 18 = 324
- 18.1 × 18.1 = 327.61
So, √325 must lie between 18.00 and 18.10. Further refining, 18.03 × 18.03 = 325.0809, which is very close to 325.
Understanding square roots is essential in algebra, geometry, and real-life applications like calculating distances, areas, or analyzing data. Rounding to two decimal places is standard in many disciplines for clarity and precision, especially in science and engineering.
So, in conclusion, the square root of 325 is approximately 18.03, and this level of approximation is generally acceptable for most practical purposes.
